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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Counting commutators


Author: R. J. Miech
Journal: Trans. Amer. Math. Soc. 189 (1974), 49-61
MSC: Primary 20F35
DOI: https://doi.org/10.1090/S0002-9947-1974-0333014-X
MathSciNet review: 0333014
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Abstract: Let G be a group generated by x and y, $ {G_2}$ be the commutator subgroup of G, and $ {G_1}$ be the group generated by y and $ {G_2}$. This paper contains explicit expansions of $ {y^{{x^m}}}$ modulo [ $ {G_2},{G_2},{G_2}$] and $ {(xy)^m}$ modulo [ $ {G_1},{G_1},{G_1}$]. The motivation for these results stem from the p-groups of maximal class, for a large number of these groups have $ [{G_1},{G_1},{G_1}] = 1$.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0333014-X
Keywords: Commutators
Article copyright: © Copyright 1974 American Mathematical Society