Data di Pubblicazione:
2023
Citazione:
Conjugacy classes of maximal cyclic subgroups / M. Bianchi, R.D. Camina, M.L. Lewis, E. Pacifici. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - (2023), pp. 1-17. [Epub ahead of print] [10.1515/jgth-2022-0134]
Abstract:
In this paper, we study the number of conjugacy classes of maximal cyclic subgroups of a finite group G, denoted n ( G ) . First we consider the properties of this invariant in relation to direct and semi-direct products, and we characterize the normal subgroups N with n ( G / N ) = n ( G ) . In addition, by applying the classification of finite groups whose nontrivial elements have prime order, we determine the structure of G / ⟨ G − ⟩ , where G − is the set of elements of G generating non-maximal cyclic subgroups of G. More precisely, we show that G / ⟨ G − ⟩ is either trivial, elementary abelian, a Frobenius group or isomorphic to A 5 .
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
conjugacy classes; maximal cyclic subgroups;
Elenco autori:
M. Bianchi, R.D. Camina, M.L. Lewis, E. Pacifici
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