Abstract
Abstract A finite š-group šŗ is said to be š-maximal if d ā¢ ( H ) < d ā¢ ( G ) d(H)<d(G) for every subgroup H < G H<G , where d ā¢ ( G ) d(G) denotes the minimal number of generators of šŗ. A similar definition can be formulated when šŗ is acted on by some group š“. In this paper, we extend earlier results of Kahn and Laffey to this more general setting and we answer a question of Berkovich on minimal non-metacyclic š-groups.
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