Counting commutators
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- by R. J. Miech PDF
- Trans. Amer. Math. Soc. 189 (1974), 49-61 Request permission
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 $[{G_1},{G_1},{G_1}] = 1$.References
- N. Blackburn, On a special class of $p$-groups, Acta Math. 100 (1958), 45–92. MR 102558, DOI 10.1007/BF02559602 P. Hall, A contribution to the theory of groups of prime power orders, Proc. London Math. Soc. 36 (1933), 29-95.
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703, DOI 10.1007/978-3-642-64981-3
- R. J. Miech, Some $p$-groups of maximal class, Trans. Amer. Math. Soc. 189 (1974), 1–47. MR 349835, DOI 10.1090/S0002-9947-1974-0349835-3
Additional Information
- © Copyright 1974 American Mathematical Society
- 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