Finite Groups with All Maximal Subgroups of Prime or Prime Square Index
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) $...
متن کاملfinite 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) $v$...
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Let G be a finite group and let δ(G) be the number of prime order subgroups of G. We determine the groups G with the property δ(G) > |G|/2− 1, extending earlier work of C. T. C. Wall, and we use our classification to obtain new results on the generation of near-rings by units of prime order. 2000 Mathematics subject classification: primary 20D06; secondary 20D10, 16Y30.
متن کاملOn subgroups of prime power index
We determine all nite groups G which admit a subgroup K of index p a ; p a prime, under the assumption that G has an irreducible and faithful GF (p)-module of dimension at most a. As an application to the theory of permutation groups we determine the maximal transitive subgroups of the primitive aane permutation groups.
متن کاملOn the Invariant Subgroups of Prime Index*
The totality formed by all the operators of any group (G) which are common to all the invariant subgroups of prime index (p) constitutes a characteristic subgroup, and the corresponding quotient group is the abelian group of order pK and of type (1, 1, 1, ■■■)-\ The number of the invariant subgroups of index p is therefore pK — 1/p — 1. The given totality includes all the operators of G which a...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 1964
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-1964-046-6