groups in which every subgroup has finite index in its frattini closure
نویسندگان
چکیده
in 1970, menegazzo [gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali, atti accad. naz. lincei rend. cl. sci. fis. mat. natur. 48 (1970), 559--562.] gave a complete description of the structure of soluble $im$-groups, i.e., groups in which every subgroup can be obtained as intersection of maximal subgroups. a group $g$ is said to have the $fm$-property if every subgroup of $g$ has finite index in the intersection $hat x$ of all maximal subgroups of $g$ containing $x$. the behaviour of (generalized) soluble $fm$-groups is studied in this paper. among other results, it is proved that if~$g$ is a (generalized) soluble group for which there exists a positive integer $k$ such that $|hat x:x|leq k$ for each subgroup $x$, then $g$ is finite-by-$im$-by-finite, i.e., $g$ contains a finite normal subgroup $n$ such that $g/n$ is a finite extension of an $im$-group.
منابع مشابه
Groups in which every subgroup has finite index in its Frattini closure
In 1970, Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 48 (1970), 559--562.] gave a complete description of the structure of soluble $IM$-groups, i.e., groups in which every subgroup can be obtained as intersection of maximal subgroups. A group $G$ is said to have the $FM$...
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عنوان ژورنال:
bulletin of the iranian mathematical societyناشر: iranian mathematical society (ims)
ISSN 1017-060X
دوره 40
شماره 5 2014
کلمات کلیدی
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