Groups of prime power order with cyclic Frattini subgroup
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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In this paper we formalized some theorems concerning the cyclic groups of prime power order. We formalize that every commutative cyclic group of prime power order is isomorphic to a direct product of family of cyclic groups [1], [18]. Let G be a finite group. The functor Ordset(G) yielding a subset of N is defined by the term (Def. 1) the set of all ord(a) where a is an element of G. One can ch...
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Let W be a finite-dimensional Z/p-module over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W ]Z/p, is called the Noether number of the representation, and is denoted by β(W ). A lower bound for β(W ) is derived, and it is shown that if U is a Z/p submodule of W , then β(U) 6 β(W ). A set of generators, in fact a SAGBI basis, is...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1980
ISSN: 1385-7258
DOI: 10.1016/1385-7258(80)90004-9