groups in which every subgroup has finite index in its frattini closure

نویسندگان

f. de giovanni

d. ‎imperatore

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.

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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 society

ناشر: iranian mathematical society (ims)

ISSN 1017-060X

دوره 40

شماره 5 2014

میزبانی شده توسط پلتفرم ابری doprax.com

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