## 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:
Laboratories: