Let eta(G) be the number of conjugacy classes of maximal cyclic subgroups of G. We prove that if G is a p-group of order p(n) and nilpotence class l, then eta(G) is bounded below by a linear function in n/l.
Conjugacy classes of maximal cyclic subgroups and nilpotence class of p-groups / M. Bianchi, R. Camina, M. Lewis. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - 106:3(2022), pp. 463-469. [10.1017/S0004972722000211]
Conjugacy classes of maximal cyclic subgroups and nilpotence class of p-groups
M. BianchiPrimo
Membro del Collaboration Group
;
2022
Abstract
Let eta(G) be the number of conjugacy classes of maximal cyclic subgroups of G. We prove that if G is a p-group of order p(n) and nilpotence class l, then eta(G) is bounded below by a linear function in n/l.
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