Endo-trivial modules: a reduction to p'-central extensions

We examine how, in prime characteristic p, the group of endotrivial modules of a finite group G and the group of endotrivial modules of a quotient of G modulo a normal subgroup of order prime to p are related. There is always an inflation map, but examples show that this map is in general not surjective. We prove that the situation is controlled by a single central extension, namely, the central extension given by a p′-representation group of the quotient of G by its largest normal p′-subgroup.


Published in:
Pacific Journal of Mathematics, 287, 2, 423-438
Year:
2017
ISSN:
0030-8730
Keywords:
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 Record created 2016-01-14, last modified 2018-03-09

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