On homomorphic images of locally graded groups
Howard Smith (1994)
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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Javier Otal, Juan Manuel Peña (1988)
Publicacions Matemàtiques
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This paper deals with one of the ways of studying infinite groups many of whose subgroups have a prescribed property, namely the consideration of minimal conditions. If P is a theoretical property of groups and subgroups, we show that a locally graded group P satisfies the minimal conditions for subgroups not having P if and only if either G is a Cernikov group or every subgroup of G satisfies P, for certain values of P concerning normality, nilpotency and related ideas.
Aynur Arikan (2007)
Rendiconti del Seminario Matematico della Università di Padova
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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.
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.
Francesco de Giovanni, Alessio Russo (2016)
Colloquium Mathematicae
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The structure of infinite groups in which any two (proper) subgroups of the same cardinality are isomorphic is described within the universe of locally graded groups. The corresponding problem for finite groups was considered by R. Armstrong (1958).
Samir Mahmoud, S. (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Huq, S.A., Aijaz, Kulsoom (1969)
Portugaliae mathematica
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Sands, A.D., Yahya, H. (2005)
Mathematica Pannonica
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Angel del Río (1990)
Publicacions Matemàtiques
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We study the weak dimension of a group-graded ring using methods developed in [B1], [Q] and [R]. We prove that if R is a G-graded ring with G locally finite and the order of every subgroup of G is invertible in R, then the graded weak dimension of R is equal to the ungraded one.
Dragomir Z. Djokovic (1979)
Journal für die reine und angewandte Mathematik
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Real, Pedro (2000)
Homology, Homotopy and Applications
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