$$\mathfrak {Z}$$ Z -permutable subgroups of finite groups
نویسندگان
چکیده
منابع مشابه
On weakly $mathfrak{F}_{s}$-quasinormal subgroups of finite groups
Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$-hypercenter of $G/H_{G}$. In this paper, we study the structur...
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A subgroup H of a finite group G is said to be W -S-permutable in G if there is a subgroup K of G such that G = HK and H ∩K is a nearly S-permutable subgroup of G. In this article, we analyse the structure of a finite group G by using the properties of W -S-permutable subgroups and obtain some new characterizations of finite p-nilpotent groups and finite supersolvable groups. Some known results...
متن کاملCOUNTING SUBGROUPS OF Z/paZ× Z/pbZ
Fix a prime p. For nonnegative integers a, b, and d, we seek a formula for the number of subgroups of order pd in Z/paZ× Z/pbZ. Set Na,b,d = #{H ⊂ Z/pZ× Z/pZ : #H = p}. This is symmetric in a and b (Na,b,d = Nb,a,d), so when it is convenient we can limit attention to the case a ≤ b. Trivially Na,b,d = 0 if d > a + b, so we may assume 0 ≤ d ≤ a + b. For 1 ≤ a ≤ b, and a + b ≥ d, we will see that...
متن کاملon weakly $mathfrak{f}_{s}$-quasinormal subgroups of finite groups
let $mathfrak{f}$ be a formation and $g$ a finite group. a subgroup $h$ of $g$ is said to be weakly $mathfrak{f}_{s}$-quasinormal in $g$ if $g$ has an $s$-quasinormal subgroup $t$ such that $ht$ is $s$-quasinormal in $g$ and $(hcap t)h_{g}/h_{g}leq z_{mathfrak{f}}(g/h_{g})$, where $z_{mathfrak{f}}(g/h_{g})$ denotes the $mathfrak{f}$-hypercenter of $g/h_{g}$. in this paper, we study the structur...
متن کاملLIFTING SUBGROUPS OF SYMPLECTIC GROUPS OVER Z/lZ
For a positive integer g, let Sp 2g(R) denote the group of 2g × 2g symplectic matrices over a ring R. Assume g ≥ 2. For a prime number l, we show that any closed subgroup of Sp 2g(Zl) that surjects onto Sp2g(Z/lZ) must in fact equal all of Sp2g(Zl). Our result is motivated by group theoretic considerations that arise in the study of Galois representations associated to abelian varieties.
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2015
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-015-0756-1