on $p$-soluble groups with a generalized $p$-central or powerful sylow $p$-subgroup

نویسندگان

evgeny khukhro

sobolev institute of mathematics, novosibirsk

چکیده

let $g$ be a finite $p$-soluble group‎, ‎and $p$ a sylow $p$-subgroup of $g$‎. ‎it is proved‎ ‎that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are‎ ‎contained in the $k$-th term of the upper central series of $p$‎, ‎then the $p$-length of‎ ‎$g$ is at most $2m+1$‎, ‎where $m$ is the greatest integer such that‎ ‎$p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$ in $g/o_{p',p}(g)$ is at most‎ ‎$p^m$‎. ‎it is also proved that if $p$ is a powerful‎ ‎$p$-group‎, ‎then the $p$-length of $g$ is equal to 1‎.

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on p-soluble groups with a generalized p-central or powerful sylow p-subgroup

let $g$ be a finite $p$-soluble group‎, ‎and $p$ a sylow $p$-sub-group of $g$‎. ‎it is proved‎ ‎that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are‎ ‎contained in the $k$-th term of the upper central series of $p$‎, ‎then the $p$-length of‎ ‎$g$ is at most $2m+1$‎, ‎where $m$ is the greatest integer such that‎ $p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$...

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عنوان ژورنال:
international journal of group theory

جلد ۱، شماره ۲، صفحات ۵۱-۵۷

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