Universal p'-central extensions

It is well-known that a finite group possesses a universal central extension if and only if it is a perfect group. Similarly, given a prime number p, we show that a finite group possesses a universal p′-central extension if and only if the p′-part of its abelianization is trivial. This question arises naturally when working with group representations over a field of characteristic p.


Published in:
Expositiones Mathematicae, 35, 3, 237-251
Year:
2017
Publisher:
Jena, Elsevier
ISSN:
0723-0869
Keywords:
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 Record created 2016-04-11, last modified 2018-03-17

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