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- Title
GROUPS IN WHICH EVERY SUBGROUP HAS FINITE INDEX IN ITS FRATTINI CLOSURE.
- Authors
DE GIOVANNI, F.; IMPERATORE, D.
- Abstract
In 1970, Menegazzo [Gruppi nei quali ogni sottogruppo è 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 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 ∣X : X∣ ⩽ 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.
- Subjects
FRATTINI subgroups; FINITE groups; SOLVABLE groups; AUTOMORPHISM groups; TORSION
- Publication
Bulletin of the Iranian Mathematical Society, 2014, Vol 40, Issue 5, p1213
- ISSN
1018-6301
- Publication type
Article