On minimal conditions related to Miller-Moreno type groups
Brunella Bruno, Richard E. Phillips (1983)
Rendiconti del Seminario Matematico della Università di Padova
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Brunella Bruno, Richard E. Phillips (1983)
Rendiconti del Seminario Matematico della Università di Padova
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Martyn Dixon, Martin Evans, Antonio Tortora (2010)
Open Mathematics
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A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.
Patrizia Longobardi, Mercede Maj, Howard Smith (1995)
Rendiconti del Seminario Matematico della Università di Padova
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Howard Smith (1994)
Rendiconti del Seminario Matematico della Università di Padova
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Aynur Arikan (2007)
Rendiconti del Seminario Matematico della Università di Padova
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Mohammad Zarrin (2015)
Colloquium Mathematicae
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We show that a locally graded group with a finite number m of non-(nilpotent of class at most n) subgroups is (soluble of class at most [log₂n] + m + 3)-by-(finite of order ≤ m!). We also show that the derived length of a soluble group with a finite number m of non-(nilpotent of class at most n) subgroups is at most [log₂ n] + m + 1.
de Giovanni, F., Russo, A., Vincenzi, G. (2002)
Serdica Mathematical Journal
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Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it...
James C. Beidleman, Derek J. S. Robinson (1992)
Rendiconti del Seminario Matematico della Università di Padova
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Patrizia Longobardi, Mercede Maj, Avinoam Mann, Akbar Rhemtulla (1996)
Rendiconti del Seminario Matematico della Università di Padova
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Russo, Francesco (2007)
International Journal of Mathematics and Mathematical Sciences
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Cansu Betin, Mahmut Kuzucuoğlu (2013)
Open Mathematics
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We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.