نتایج جستجو برای: finite p group
تعداد نتایج: 2207141 فیلتر نتایج به سال:
a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$ implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some authors. recently, podoski and szegedy proved the truth of the converse of schur's theorem for capable groups. they also established an explicit bound for the index of the center of such...
let $g$ be a non-abelian group of order $p^n$, where $nleq 5$ in which $g$ is not extra special of order $p^5$. in this paper we determine the maximal size of subsets $x$ of $g$ with the property that $xyneq yx$ for any $x,y$ in $x$ with $xneq y$.
Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and on...
It is proved that for any prime p a finitely generated nilpotent group is conjugacy separable in the class of finite p-groups if and only if the tor-sion subgroup of it is a finite p-group and the quotient group by the torsion subgroup is abelian. 1. Let K be a class of groups. A group G is called residual K (or K-residual) if for each non-unit element a ∈ G there is a homomorphism ϕ of G onto ...
For a finite group G, let cd(G) be the set of irreducible complex character degrees of G forgetting multiplicities and X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Suppose that p is a prime number. We prove that if G is a finite group such that |G| = |PGL(2, p)|, p ∈ cd(G) and max(cd(G)) = p+1, then G ∼= PGL(2, p), SL(2, p) or PSL(2, p) × A, where ...
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