Following publication of the original article 1, the author reported his family name has been marked as the first name. His given name is M. Kumi and his family name is Smith.
We construct a supercharacter theory, and establish the supercharacter table for Sylow p-subgroups of the Chevalley groups of Lie type when p>2. Then we calculate the conjugacy classes, determine the ...complex irreducible characters by Clifford theory, and obtain the character tables for when p>3.
Let Formula omitted. be a partition of the set of all primes Formula omitted. and G a finite group. A set Formula omitted. of subgroups of G is said to be a complete Hall σ-set of G if every member ...Formula omitted. of Formula omitted. is a Hall σi-subgroup of G for some Formula omitted. and Formula omitted. contains exactly one Hall σi-subgroup of G for every i such that Formula omitted. . A group is said to be σ-primary if it is a finite σi-group for some i. A subgroup A of G is said to be: σ-permutable in G if G possesses a complete Hall σ-set Formula omitted. such that Formula omitted. for all Formula omitted. and all Formula omitted. ; Formula omitted. -subnormal in G if there is a subgroup chain Formula omitted. such that either Formula omitted. or Formula omitted. is σ-primary for all Formula omitted. . We say that a subgroup H of G is: m-σ-permutable in G if Formula omitted. for some modular subgroup A and σ-permutable subgroup B of G; weakly m-σ-permutable in G if there are an m-σ-permutable subgroup S and a σ-subnormal subgroup T of G such that G = HT and Formula omitted. .We study G assuming that some subgroups of G are weakly m-σ-permutable in G.
Let σ be some partition of the set of all primes and Formula omitted. a complete Hall σ-set of a finite group G. A subgroup H of G is said to be σ-conditionally permutable in G if for any subgroup ...Formula omitted. there exists an element Formula omitted. such that Formula omitted. In this article, we investigate the influence of σ-conditionally permutable subgroups on the structure of finite groups.
In this paper, we characterize and compute the mixed and non-mixed basis of Dihedral groups. Also, by computing the conjugacy classes, we describe all the mixed and non-mixed normal subgroups of ...Dihedral Groups.
Let G be a finite group and σ = {σi|ielement ofI} some partition of the set of all primes. A subgroup A of G is said to be generalized σ-subnormal in G if A = <L,T>, where L is a modular subgroup and ...T is a σ-subnormal subgroup of G. In this paper, we prove that if every Schmidt subgroup of G is generalized σ-subnormal in G, then the commutator subgroup Gvprime of G is σ-nilpotent.
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