Finite groups with prime $p$ to the first power

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) $...

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) $v$...

Some Results on Finite Groups Whose Order Contains a Prime to the First Power

In a previous investigation [1], the author has studied finite groups © of an order g = pgo where p is a prime and go an integer not divisible by p. This work has been continued by H. F. Tuan [51 Let t denote the number of conjugate classes of ® which consist of element of order p. Tuan dealt with the groups ® for which t^2 and which have a faithful representation of degree less than p 1. We sh...

Finite Groups with p-Sylow Coverings

Finite Simple Groups with Narrow Prime Spectrum

We find the nonabelian finite simple groups with order prime divisors not exceeding 1000. More generally, we determine the sets of nonabelian finite simple groups whose maximal order prime divisor is a fixed prime less than 1000. Our results are based on calculations in the computer algebra system GAP.