@article {
author = {De Giovanni, F. and Imperatore, D.},
title = {Groups in which every subgroup has finite index in its Frattini closure},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {40},
number = {5},
pages = {1213-1226},
year = {2014},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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.},
keywords = {Maximal subgroup,Frattini closure,$FM$-group},
url = {http://bims.iranjournals.ir/article_561.html},
eprint = {http://bims.iranjournals.ir/article_561_3a8e1901acbb88df60bd42b42c8fb15d.pdf}
}