Abstract
We study finite groups whose every subset containing the identity and closed with respect to the operation x ○ y = xy −1 x is a subgroup. We prove that the derived subgroup of such a group is nilpotent, which implies that the derived length of such a group is at most three.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 5, pp. 1117–1127, September–October, 2006.
Original Russian Text Copyright © 2006 Myl’nikov A. L.
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Myl’nikov, A.L. Nilpotency of the derived subgroup of a finite tangled group. Sib Math J 47, 915–923 (2006). https://doi.org/10.1007/s11202-006-0102-x
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DOI: https://doi.org/10.1007/s11202-006-0102-x