On the derived length of finite, graded Lie rings with prime-power order, and groups with prime-power order
نویسندگان
چکیده
منابع مشابه
Finite groups with $X$-quasipermutable subgroups of prime power order
Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $...
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let $h$, $l$ and $x$ be subgroups of a finite group$g$. then $h$ is said to be $x$-permutable with $l$ if for some$xin x$ we have $al^{x}=l^{x}a$. we say that $h$ is emph{$x$-quasipermutable } (emph{$x_{s}$-quasipermutable}, respectively) in $g$ provided $g$ has a subgroup$b$ such that $g=n_{g}(h)b$ and $h$ $x$-permutes with $b$ and with all subgroups (with all sylowsubgroups, respectively) $v$...
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متن کاملGroups of prime-power order with a small second derived quotient
For odd primes we prove some structure theorems for finite p-groupsG, such that G′′ 6= 1 and |G′/G′′| = p. Building on results of Blackburn and Hall, it is shown that γ3(G) is a maximal subgroup of G ′, the group G has a central decomposition into two simpler subgroups, and, moreover, G′ has one of two isomorphism types.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2001
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700019791