Difference sets disjoint from a subgroup II: groups of order 4p²

2021/03/17 by Humphries, Stephen P., Nicholson, Nathan L.
#05B10 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2103.09892

Abstract

We study finite groups G having a normal subgroup H and D ⊂ G ∖ H, D ∩ D^-1=∅, such that the multiset \ xy^-1:x,y ∈ D\ has every non-identity element occur the same number of times (such a D is called a \it DRAD difference set). We show that there are no such groups of order 4p², where p is an odd prime.

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