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math.GR2023
Totally deranged elements of almost simple groups and invariable generating sets
Scott Harper
By a classical theorem of Jordan, every faithful transitive action of a nontrivial finite group has a derangement (an element with no fixed points). The existence of derangements w…
math.GR2023
The maximal size of a minimal generating set
Scott Harper
A generating set for a finite group is said to be minimal if no proper subset generates , and denotes the maximal size of a minimal generating set for . We prove a…