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Information Journal Paper

Title

GROUPS IN WHICH EVERY SUBGROUP HAS FINITE INDEX IN ITS FRATTINI CLOSURE

Pages

  1213-1226

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 xÙ 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 ifG is a (generalized) soluble group for which there exists a positive integerk such that |xÙ: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.

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    • Cite

    APA: Copy

    DE GIOVANNI, FRANCESCO, & IMPERATORE, DIANA. (2014). GROUPS IN WHICH EVERY SUBGROUP HAS FINITE INDEX IN ITS FRATTINI CLOSURE. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 40(5), 1213-1226. SID. https://sid.ir/paper/636369/en

    Vancouver: Copy

    DE GIOVANNI FRANCESCO, IMPERATORE DIANA. GROUPS IN WHICH EVERY SUBGROUP HAS FINITE INDEX IN ITS FRATTINI CLOSURE. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2014;40(5):1213-1226. Available from: https://sid.ir/paper/636369/en

    IEEE: Copy

    FRANCESCO DE GIOVANNI, and DIANA IMPERATORE, “GROUPS IN WHICH EVERY SUBGROUP HAS FINITE INDEX IN ITS FRATTINI CLOSURE,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 40, no. 5, pp. 1213–1226, 2014, [Online]. Available: https://sid.ir/paper/636369/en

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