For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G i...For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.展开更多
Let P be a finite group and denote by w（P） the set of its element orders. P is called k-recognizable by the set of its element orders if for any finte group G with ω（G） =ω（P） there are, up to isomorphism, k fi...Let P be a finite group and denote by w（P） the set of its element orders. P is called k-recognizable by the set of its element orders if for any finte group G with ω（G） =ω（P） there are, up to isomorphism, k finite groups G such that G ≌P. In this paper we will prove that the group Lp（3）, where p 〉 3 is a prime number, is at most 2-recognizable.展开更多
For G a finite group,π_e(G)denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω)stands for the number of isomorphism classes of finite groups with the same set Ω of element...For G a finite group,π_e(G)denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω)stands for the number of isomorphism classes of finite groups with the same set Ω of element orders.We say that G is k-distinguishable if h(π_(G))=k<∞,otherwise G is called non-distinguishable.Usually,a 1-distinguishable group is called a characterizable group.It is shown that if M is a sporadic simple group different from M_(12),M_(22),J_2,He,Suz,M^cL and O'N, then Aut(M)is charaeterizable by its dement orders.It is also proved that if M is isomorphic to M_(12),M_(22),He,Suz or O'N,then h(π_e(Aut(M)))∈{1,∞}.展开更多
The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we...The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we will prove OC（G） = OC（^2Dp（3）） if and only if G is isomorphic to ^2Dp（3）. A main consequence of our result is the validity of Thompson＇s conjecture for the groups under consideration.展开更多
In this paper we determine all tetravalent Cayley graphs of a non-abelian group of order 3p2, where p is a prime number greater than 3, and with a cyclic Sylow p-subgroup. We show that all of these tetravalent Cayley ...In this paper we determine all tetravalent Cayley graphs of a non-abelian group of order 3p2, where p is a prime number greater than 3, and with a cyclic Sylow p-subgroup. We show that all of these tetravalent Cayley graphs are normal. The full automorphism group of these Cayley graphs is given and the half-transitivity and the arc-transitivity of these graphs are investigated. We show that this group is a 5-CI-group.展开更多
基金This work has been supported by the Research Institute for Fundamental Sciences Tabriz,Iran.
文摘For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.
基金Supported by the research council of College of Science, the University of Tehran (Grant No. 6103014-1-03)
文摘Let P be a finite group and denote by w（P） the set of its element orders. P is called k-recognizable by the set of its element orders if for any finte group G with ω（G） =ω（P） there are, up to isomorphism, k finite groups G such that G ≌P. In this paper we will prove that the group Lp（3）, where p 〉 3 is a prime number, is at most 2-recognizable.
基金This work has been partially sopported by the Research Institute for Fundamental Sciences Tabriz,Iran
文摘For G a finite group,π_e(G)denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω)stands for the number of isomorphism classes of finite groups with the same set Ω of element orders.We say that G is k-distinguishable if h(π_(G))=k<∞,otherwise G is called non-distinguishable.Usually,a 1-distinguishable group is called a characterizable group.It is shown that if M is a sporadic simple group different from M_(12),M_(22),J_2,He,Suz,M^cL and O'N, then Aut(M)is charaeterizable by its dement orders.It is also proved that if M is isomorphic to M_(12),M_(22),He,Suz or O'N,then h(π_e(Aut(M)))∈{1,∞}.
文摘The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we will prove OC（G） = OC（^2Dp（3）） if and only if G is isomorphic to ^2Dp（3）. A main consequence of our result is the validity of Thompson＇s conjecture for the groups under consideration.
文摘In this paper we determine all tetravalent Cayley graphs of a non-abelian group of order 3p2, where p is a prime number greater than 3, and with a cyclic Sylow p-subgroup. We show that all of these tetravalent Cayley graphs are normal. The full automorphism group of these Cayley graphs is given and the half-transitivity and the arc-transitivity of these graphs are investigated. We show that this group is a 5-CI-group.
