On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center
Group Theory
2023-06-13 v1 Representation Theory
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.
Keywords
Cite
@article{arxiv.2306.06957,
title = {On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center},
author = {Diego García-Lucas and Leo Margolis},
journal= {arXiv preprint arXiv:2306.06957},
year = {2023}
}