on p-soluble groups with a generalized p-central or powerful sylow p-subgroup
نویسندگان
چکیده
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 $p$ 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.
منابع مشابه
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 $p$-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 $p$...
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عنوان ژورنال:
international journal of group theoryناشر: university of isfahan
ISSN 2251-7650
دوره 1
شماره 2 2012
کلمات کلیدی
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