Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and ...Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and H containsexactly one Hallσi-subgroup of G for every i such thatσi∩π(G)≠Ø.A subgroupA of G is said to be H-permutable if A permutes with all members of the completeHallσ-set H of G.In this paper,we study the structure of G under the assuming thatsome subgroups of G areσ-permutable.展开更多
In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices...In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices,and inversesemigroups.As an application of our results,we also show that the unary operations*:Hg→Hg-1 Hg and*:Hg→HG on the coset semigroupK(G)of a group G are-condensing operators.Consequently,a necessary and sufficient condition for theseoperators to be 69-condensing operators is given.Some further results on condensesemigroups considered by Chen et al.(Acta Math.Hung.119:281-305,2008)arediscussed and obtained in this paper.展开更多
The authors determine all the complete Langlands parameters corresponding to the representations of the classical groups with integral regular infintesimal characters, and get all L-packts in that case.
基金a NNSF grant of China(Grant#11371335)Wu Wen-TsunKey Laboratory of Mathematics of Chinese Academy of Sciences.Research of the third author is supported by Chinese Academy of Sciences Visiting Professorship for Senior International Scientists(Grant No.2010T2J12).
文摘Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and H containsexactly one Hallσi-subgroup of G for every i such thatσi∩π(G)≠Ø.A subgroupA of G is said to be H-permutable if A permutes with all members of the completeHallσ-set H of G.In this paper,we study the structure of G under the assuming thatsome subgroups of G areσ-permutable.
基金the Grants of Natural Scientific Foundation of China(Nos.61572013 and 61272196).
文摘In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices,and inversesemigroups.As an application of our results,we also show that the unary operations*:Hg→Hg-1 Hg and*:Hg→HG on the coset semigroupK(G)of a group G are-condensing operators.Consequently,a necessary and sufficient condition for theseoperators to be 69-condensing operators is given.Some further results on condensesemigroups considered by Chen et al.(Acta Math.Hung.119:281-305,2008)arediscussed and obtained in this paper.
文摘The authors determine all the complete Langlands parameters corresponding to the representations of the classical groups with integral regular infintesimal characters, and get all L-packts in that case.
