### فهرست مطالب

• Volume:6 Issue:4, 2017
• تاریخ انتشار: 1396/06/21
• تعداد عناوین: 5
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• Behnam Ebrahimzadeh, Ali Iranmanesh *, Hosein Parvizi Mosaed Pages 1-6
In this paperý, ýwe prove that Ree group 2G2(q)ý, ýwhere q±3q−−√ is a prime number can be uniquely determined by the order of group and the number of elements with the same orderý.
Keywords: Element order?, ?Prime graph?, ?Ree group?
• Alexey Staroletov* Pages 7-33
The set of element orders of a finite group G is called the {\em spectrum}ý. ýGroups with coinciding spectra are said to be {\em isospectral}ý. ýIt is known that if G has a nontrivial normal soluble subgroup then there exist infinitely many pairwise non-isomorphicý ýgroups isospectral to Gý. ýThe situation is quite different if G is a nonabelain simple groupý. ýRecently it was proved that if L is a simple classical group of dimension at least 62 and G is a finite groupý ýisospectral to Lý, ýthen up to isomorphism L≤G≤\AutLý. ýWe show that the assertion remains trueý ýif 62 is replaced by 38ý.
Keywords: ýSimple classical groupsý, ýElement ordersý, ýPrime graph of a finite groupý, ýAlmost recognizable group
• Hamid Mousavi, Zahra Rezazadeh Pages 35-40
For a finite group Gý, ýlet νnc(G) denote the number of conjugacy classes of non-normal non-cyclic subgroups of G ý. ýWe characterize the finite non-nilpotent groups whose all non-normal non-cyclic subgroups are conjugateý.
Keywords: ýNon-normal subgroups, Conjugacy classes of non-normal subgroups, Non-nilpotent groups
• Roghayeh Hafezieh* Pages 41-51
Let G be a finite groupý. ýWe consider the set of the irreducible complex characters of Gý, ýnamely Irr(G)ý, ýand the related degree set cd(G)={χ(1)ý:ýχ∈Irr(G)}ý. ýLet ρ(G) be the set of all primes which divide some character degree of Gý. ýIn this paper we introduce the bipartite divisor graph for cd(G) as an undirected bipartite graph with vertex set ρ(G)∪(cd(G)∖{1})ý, ýsuch that an element p of ρ(G) is adjacent to an element m of cd(G)∖{1} if and only if p divides mý. ýWe denote this graph simply by B(G)ý. ýThen by means of combinatorial properties of this graphý, ýwe discuss the structure of the group Gý. ýIn particularý, ýwe consider the cases where B(G) is a path or a cycleý.
Keywords: ýbipartite divisor graphý, ýirreducible character degreeý, ýpathý, ýcycle
• Zwelethemba Mpono* Pages 53-58
M24 is the largest Mathieu sporadic simple group of order 244823040=210⋅33⋅5⋅7⋅11⋅23 and contains all the other Mathieu sporadic simple groups as subgroups. The object in this paper is to study the ranks of M24 with respect to the conjugacy classes of all its nonidentity elements.
Keywords: Rank, Generations, structure constants, class fusions, maximal subgroups