TY - JOUR
T1 - Powers in finite groups and a criterion for solubility
AU - Liebeck, Martin W.
AU - Shalev, Aner
PY - 2013
Y1 - 2013
N2 - We study the set G[k] of kth powers in finite groups G. We prove that if G[12] is a subgroup, then G must be soluble; moreover, 12 is the minimal number with this property. The proof relies on results of independent interest, classifying almost simple groups G and positive integers k for which G[k] contains the socle of G.
AB - We study the set G[k] of kth powers in finite groups G. We prove that if G[12] is a subgroup, then G must be soluble; moreover, 12 is the minimal number with this property. The proof relies on results of independent interest, classifying almost simple groups G and positive integers k for which G[k] contains the socle of G.
UR - http://www.scopus.com/inward/record.url?scp=84884738187&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2013-11790-9
DO - 10.1090/S0002-9939-2013-11790-9
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AN - SCOPUS:84884738187
SN - 0002-9939
VL - 141
SP - 4179
EP - 4189
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 12
ER -