Higher commutativity and nilpotency in finite groups
نویسندگان
چکیده
منابع مشابه
Finite groups with three relative commutativity degrees
For a finite group $G$ and a subgroup $H$ of $G$, the relative commutativity degree of $H$ in $G$, denoted by $d(H,G)$, is the probability that an element of $H$ commutes with an element of $G$. Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$. It is shown that a finite group $G$ admits three relative commutativity degrees if a...
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we consider two commutativity ratios $pr(g)$ and $f(g)$ in a finite group $g$ and examine the properties of $g$ when these ratios are `large'. we show that if $pr(g) > frac{7}{24}$, then $g$ is metabelian and we give threshold results in the cases where $g$ is insoluble and $g'$ is nilpotent. we also show that if $f(g) > frac{1}{2}$, then $f(g) = frac{n+1}{2n}$, for some na...
متن کاملON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS
Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...
متن کاملfinite groups with three relative commutativity degrees
for a finite group $g$ and a subgroup $h$ of $g$, the relative commutativity degree of $h$ in $g$, denoted by $d(h,g)$, is the probability that an element of $h$ commutes with an element of $g$. let $mathcal{d}(g)={d(h,g):hleq g}$ be the set of all relative commutativity degrees of subgroups of $g$. it is shown that a finite group $g$ admits three relative commutativity degrees if a...
متن کاملPrimary subgroups and p-nilpotency of finite groups
In this paper, we investigate the influence of Ssemipermutable and weakly S-supplemented subgroups on the pnilpotency of finite groups. Some recent results are generalized. Keywords—S-semipermutable, weakly S-supplemented, pnilpotent.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2012
ISSN: 0024-6093
DOI: 10.1112/blms/bds055