The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regu...The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.展开更多
This paper computes the group and character table of Trimethylborane and Cyclohaxane. Results show that the groups are isomorphic to the wreath products C3wrC2 and C2wrC6 with orders 81 and 384 and with 17 and 28 conj...This paper computes the group and character table of Trimethylborane and Cyclohaxane. Results show that the groups are isomorphic to the wreath products C3wrC2 and C2wrC6 with orders 81 and 384 and with 17 and 28 conjugacy classes respectively, where Cn denotes a cyclic group of order n.展开更多
In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and re...In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and relator sets for , and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).展开更多
In this paper, we showed how groups are embedded into wreath products, we gave a simpler proof of the theorem by Audu (1991) (see <a href="#ref1">[1]</a>), also proved that a group can be embedde...In this paper, we showed how groups are embedded into wreath products, we gave a simpler proof of the theorem by Audu (1991) (see <a href="#ref1">[1]</a>), also proved that a group can be embedded into the wreath product of a factor group by a normal subgroup and also proved that a factor group can be embedded inside a wreath product and the wreath product of a factor group by a factor group can be embedded into a group. We further showed that when the abstract group in the Universal Embedding Theorem is a <em>p</em>-group, cyclic and simple, the embedding becomes an isomorphism. Examples were given to justify the results.展开更多
This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field F_(q), which are functions F_(q)→F_(q) that agree with a suitable monomial function x↦axr on each coset of the index d ...This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field F_(q), which are functions F_(q)→F_(q) that agree with a suitable monomial function x↦axr on each coset of the index d subgroup of F_(q)^(*). We discuss two important rewriting procedures in the context of generalized cyclotomic mappings and present applications thereof that concern index d generalized cyclotomic permutations of F_(q) and pertain to cycle structures, the classification of (q−1)-cycles and involutions, as well as inversion.展开更多
Let G = NwrA be a wreath product of a finite nilpotent group N by an abelian group A. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result,it is obtaine...Let G = NwrA be a wreath product of a finite nilpotent group N by an abelian group A. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result,it is obtained that the normalizer property holds for G.展开更多
Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz numbers.We prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand...Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz numbers.We prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand-join equation.Furthermore,H G·(t;p +,p) is a product of several copies of tau functions of the 2-Toda hierarchy,in independent variables.These generalize the corresponding results for ordinary Hurwitz numbers.展开更多
Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on com...Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on completely regular semigroups.In this paper,we give one class of congruences on completely regular semigroups with the representation of wreath product of translational hulls on completely simple semigroups.By this new way,the least Clifford semigroup congruences on completely regular semigroups are generalized.展开更多
In this paper, we generate the wreath product L2 (1 1) wrM12 using only two permutations. Also, we show the structure of some groups containing the wreath product L2(1 1)wrM12. The structure of the groups founded ...In this paper, we generate the wreath product L2 (1 1) wrM12 using only two permutations. Also, we show the structure of some groups containing the wreath product L2(1 1)wrM12. The structure of the groups founded is determined in terms of wreath product (L2 (11)wrM12)wrCt. Some related cases are also included. Also, we will show that S132K+1 and A132K+l can be generated using the wreath product (L2 (1 1)wrM12) wr Ck and a transposition in S132K+1 and an element of order 3 in A132K+l. We will also show that S132K+1 and A132K+1 can be generated using the wreath product L2 (1 1) wrMl2 and an element of order k + 1.展开更多
This paper presents a character table of S_4 wr S_2 wreath product group.Using this character table,~1H or ^(13)C NMR spectra analysis of molecula with S_4[S_2]symmetry,especially simplification of the secular determi...This paper presents a character table of S_4 wr S_2 wreath product group.Using this character table,~1H or ^(13)C NMR spectra analysis of molecula with S_4[S_2]symmetry,especially simplification of the secular determinant equation will be easy to carry out. Molecules with S_4[S_2]symmetry,are exemplified by octaphenylcyclo- tetrasiloxane and 2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine chromium (Ⅲ)chloride.展开更多
In this note the authors investigates the property of the GF(2)-modules for the wreath products Sz(q)wrCt,and establish some sufficient condition for a Sz(q)wrCt, GF(2)-module to be natural.
文摘The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.
文摘This paper computes the group and character table of Trimethylborane and Cyclohaxane. Results show that the groups are isomorphic to the wreath products C3wrC2 and C2wrC6 with orders 81 and 384 and with 17 and 28 conjugacy classes respectively, where Cn denotes a cyclic group of order n.
文摘In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and relator sets for , and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).
文摘In this paper, we showed how groups are embedded into wreath products, we gave a simpler proof of the theorem by Audu (1991) (see <a href="#ref1">[1]</a>), also proved that a group can be embedded into the wreath product of a factor group by a normal subgroup and also proved that a factor group can be embedded inside a wreath product and the wreath product of a factor group by a factor group can be embedded into a group. We further showed that when the abstract group in the Universal Embedding Theorem is a <em>p</em>-group, cyclic and simple, the embedding becomes an isomorphism. Examples were given to justify the results.
文摘This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field F_(q), which are functions F_(q)→F_(q) that agree with a suitable monomial function x↦axr on each coset of the index d subgroup of F_(q)^(*). We discuss two important rewriting procedures in the context of generalized cyclotomic mappings and present applications thereof that concern index d generalized cyclotomic permutations of F_(q) and pertain to cycle structures, the classification of (q−1)-cycles and involutions, as well as inversion.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171169, 11071155)Natural Science Foundation of Shandong Province (Grant No. Y2008A03)Shandong Provincial Education Department (Grant No. J07YH06)
文摘Let G = NwrA be a wreath product of a finite nilpotent group N by an abelian group A. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result,it is obtained that the normalizer property holds for G.
基金supported by National Natural Science Foundation of China(Grant Nos.10425101,10631050)National Basic Research Program of China(973Project)(Grant No.2006cB805905)
文摘Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz numbers.We prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand-join equation.Furthermore,H G·(t;p +,p) is a product of several copies of tau functions of the 2-Toda hierarchy,in independent variables.These generalize the corresponding results for ordinary Hurwitz numbers.
基金National Natural Science Foundation of China(No.11671056)General Science Foundation of Shanghai Normal University,China(No.KF201840)。
文摘Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on completely regular semigroups.In this paper,we give one class of congruences on completely regular semigroups with the representation of wreath product of translational hulls on completely simple semigroups.By this new way,the least Clifford semigroup congruences on completely regular semigroups are generalized.
文摘In this paper, we generate the wreath product L2 (1 1) wrM12 using only two permutations. Also, we show the structure of some groups containing the wreath product L2(1 1)wrM12. The structure of the groups founded is determined in terms of wreath product (L2 (11)wrM12)wrCt. Some related cases are also included. Also, we will show that S132K+1 and A132K+l can be generated using the wreath product (L2 (1 1)wrM12) wr Ck and a transposition in S132K+1 and an element of order 3 in A132K+l. We will also show that S132K+1 and A132K+1 can be generated using the wreath product L2 (1 1) wrMl2 and an element of order k + 1.
文摘This paper presents a character table of S_4 wr S_2 wreath product group.Using this character table,~1H or ^(13)C NMR spectra analysis of molecula with S_4[S_2]symmetry,especially simplification of the secular determinant equation will be easy to carry out. Molecules with S_4[S_2]symmetry,are exemplified by octaphenylcyclo- tetrasiloxane and 2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine chromium (Ⅲ)chloride.
文摘In this note the authors investigates the property of the GF(2)-modules for the wreath products Sz(q)wrCt,and establish some sufficient condition for a Sz(q)wrCt, GF(2)-module to be natural.
基金supported by the National Natural Science Foundation of China(Nos.11226122,11301224,11231002)the Zhejiang Provincial Natural Science Foundation of China(No.LQ12A01015)
文摘The authors use geometric techniques to prove that the restricted wreath product F■Z is a quasi-isometrically embedded subgroup of Thompson's group F.