TY - CHAP
T1 - Log-space complexity of the conjugacy problem in wreath products
AU - Myasnikov, Alexei
AU - Vassileva, Svetla
AU - Weiss, Armin
N1 - Publisher Copyright:
© 2018 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
PY - 2017/12/26
Y1 - 2017/12/26
N2 - We show a transfer result from individual groups to wreath products. Namely, we prove that the conjugacy problem in the wreath product AB of two groups A and B is log-space decidable, provided the factor groups A and B both have log-space decidable conjugacy problem and B has log-space computable power problem. If, additionally, A and B have bounded torsion and A has log-space computable power problem, we show that the iterated wreath product AnB also has log-space decidable conjugacy problem. We apply these general results to show that free solvable groups and wreath products of two abelian groups (in particular, the lamplighter group, Z2 = Z) have log-space decidable conjugacy problem.
AB - We show a transfer result from individual groups to wreath products. Namely, we prove that the conjugacy problem in the wreath product AB of two groups A and B is log-space decidable, provided the factor groups A and B both have log-space decidable conjugacy problem and B has log-space computable power problem. If, additionally, A and B have bounded torsion and A has log-space computable power problem, we show that the iterated wreath product AnB also has log-space decidable conjugacy problem. We apply these general results to show that free solvable groups and wreath products of two abelian groups (in particular, the lamplighter group, Z2 = Z) have log-space decidable conjugacy problem.
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M3 - Chapter
AN - SCOPUS:85045607525
SN - 9789813204041
SP - 215
EP - 236
BT - Infinite Group Theory
ER -