نتایج جستجو برای: non abelian simple group
تعداد نتایج: 2537999 فیلتر نتایج به سال:
the theorem 12 in [a note on $p$-nilpotence and solvability of finite groups, j. algebra 321(2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indice. in this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index aresolvable.
Let $G$ be a finite non-abelian group with center $Z(G)$. The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $Gsetminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy ne yx$. In this paper, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups..
let $gamma$ be a normal subgroup of the full automorphism group $aut(g)$ of a group $g$, and assume that $inn(g)leq gamma$. an endomorphism $sigma$ of $g$ is said to be {it $gamma$-central} if $sigma$ induces the the identity on the factor group $g/c_g(gamma)$. clearly, if $gamma=inn(g)$, then a $gamma$-central endomorphism is a {it central} endomorphism. in this article the conditi...
Let $G$ be a finite group. A subset $X$ of $G$ is a set of pairwise non-commuting elements if any two distinct elements of $X$ do not commute. In this paper we determine the maximum size of these subsets in any finite non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup.
In this paper we prove that a finite group $G$ having at most three conjugacy classes of non-normal non-abelian proper subgroups is always solvable except for $Gcong{rm{A_5}}$, which extends Theorem 3.3 in [Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable, Acta Math. Sinica (English Series) 27 (2011) 891--896.]. Moreover, we s...
let $g$ be a finite group. a subset $x$ of $g$ is a set of pairwise non-commuting elements if any two distinct elements of $x$ do not commute. in this paper we determine the maximum size of these subsets in any finite non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup.
in [u. dempwolff, on extensions of elementary abelian groups of order $2^{5}$ by $gl(5,2)$, textit{rend. sem. mat. univ. padova}, textbf{48} (1972), 359 - 364.] dempwolff proved the existence of a group of the form $2^{5}{^{cdot}}gl(5,2)$ (a non split extension of the elementary abelian group $2^{5}$ by the general linear group $gl(5,2)$). this group is the second l...
it was shown in [a. azimifard, e. samei, n. spronk, jfa 256 (2009)] that the zl-amenability constant of a finite group is always at least~$1$, with equality if and only if the group is abelian. it was also shown in [a. azimifard, e. samei, n. spronk, op cit.] that for any finite non-abelian group this invariant is at least $301/300$, but the proof relies crucially on a deep result of d. a. ride...
given an integer $n$, we denote by $mathfrak b_n$ and $mathfrak c_n$ the classes of all groups $g$ for which the map $phi_{n}:gmapsto g^n$ is a monomorphism and an epimorphism of $g$, respectively. in this paper we give a characterization for groups in $mathfrak b_n$ and for groups in $mathfrak c_n$. we also obtain an arithmetic description of the set of all integers $n$ such that a gr...
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