Independent sets of generators of prime power order

2021/01/15 by Lucchini, Andrea, Spiga, Pablo
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2101.06226

Abstract

A subset X of a finite group G is said to be prime-power-independent if each element in X has prime power order and there is no proper subset Y of X with ⟨ Y, Φ(G)⟩ = ⟨ X, Φ(G)⟩, where Φ(G) is the Frattini subgroup of G. A group G is B_pp if all prime-power-independent generating sets for G have the same cardinality. We prove that, if G is B_pp, then G is solvable. Pivoting on some recent results of Krempa and Stocka, this yields a complete classification of B_pp-groups.

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