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 -