On locally soluble periodic groups with Chernikov centralizer of a four-subgroup
نویسندگان
چکیده
منابع مشابه
Topologically Locally Finite Groups with a CC-Subgroup
A proper subgroup M of a finite group G is called a CCsubgroup of G if the centralizer CG(m) of every m ∈ M = M \ {1} is contained in M . Such finite groups had been partially classified by S.Williams, A. S.Kondrat’iev, N. Iiyori and H.Yamaki, M. Suzuki, W.Feit and J. G.Thompson, M.Herzog, Z.Arad, D.Chillag and others. In [6] the present authors, having taken all this work into account, classif...
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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 $p$...
متن کاملon 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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The c-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite cdimension k is soluble of derived length bounded in terms of k, and the rank of its quotient by the Hirsch–Plotkin radical is bounded in terms of k. Corollary: a pseudo-(finite soluble) group of finite c-dimension k is soluble of derived length bounde...
متن کاملlocally finite p-groups with all subgroups either subnormal or nilpotent-by-chernikov
we pursue further our investigation, begun in [h.~smith, groups with all subgroups subnormal or nilpotent-by-{c}hernikov, emph{rend. sem. mat. univ. padova} 126 (2011), 245--253] and continued in [g.~cutolo and h.~smith, locally finite groups with all subgroups subnormal or nilpotent-by-{c}hernikov. emph{centr. eur. j. math.} (to appear)] of groups $g$ in w...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1994
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500018757