In this paper, we set eta(G) to be the number of conjugacy classes of maximal cyclic subgroups of a finite group G. We compute eta(G) for all metacyclic p-groups. We show that if G is a metacyclic p-group of order p(n) that is not dihedral, generalized quaternion, or semi-dihedral, then eta(G) >= n - 2, and we determine when equality holds.
Conjugacy classes of maximal cyclic subgroups of metacyclic p-groups / M. Bianchi, R. Camina, M. Lewis. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - (2022), pp. 1-22. [Epub ahead of print] [10.1515/jgth-2022-0103]
Conjugacy classes of maximal cyclic subgroups of metacyclic p-groups
M. Bianchi
Primo
Membro del Collaboration Group
;
2022
Abstract
In this paper, we set eta(G) to be the number of conjugacy classes of maximal cyclic subgroups of a finite group G. We compute eta(G) for all metacyclic p-groups. We show that if G is a metacyclic p-group of order p(n) that is not dihedral, generalized quaternion, or semi-dihedral, then eta(G) >= n - 2, and we determine when equality holds.File in questo prodotto:
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