On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center

2023/06/12 by García-Lucas, Diego, Margolis, Leo · 1 citation
#16S34 #16U60 #20C05 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2306.06957

Abstract

We show that the modular isomorphism problem has a positive answer for groups of nilpotency class 2 with cyclic center, i.e. that for such p-groups G and H an isomorphism between the group algebras FG and FH implies an isomorphism of the groups G and H for F the field of p elements. For groups of odd order this implication is also proven for F being any field of characteristic p. For groups of even order we need either to make an additional assumption on the groups or on the field.

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