FINITE GROUPS WITH INDEPENDENT GENERATING SETS OF ONLY TWO SIZES
Andrea Lucchini, Pablo Spiga · Bulletin of the Australian Mathematical Society · 2023
Abstract A generating set S for a group G is independent if the subgroup generated by $S\setminus \{s\}$ is properly contained in G for all $s \in S.$ We describe the structure of finite groups G such that there are precisely two numbers appearing as the cardinalities of independent generating sets for G.