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An Algorithmic Solution for a Word Problem in Group Theory

Published online by Cambridge University Press:  20 November 2018

N. S. Mendelsohn
N. S. Mendelsohn*
Affiliation:
University of Manitoba, Winnipeg
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This paper describes a systematic procedure which yields in a finite number of steps a solution to the following problem. Let G be a group generated by a finite set of generators g1, g2, g3, . . . , gr and defined by a finite set of relations R1 = R2 = . . . = Rk = I, where I is the unit element of G and R1R2, . . . , Rk are words in the gi and gi-1. Let H be a subgroup of G, known to be of finite index, and generated by a finite set of words, W1, W2, . . . , Wt. Let W be any word in G. Our problem is the following. Can we find a new set of generators for H, together with a set of representatives h1 = 1, h2, . . . , hu of the right cosets of H (i.e. G = H1 + Hh2 + . . . + Hhu) such that W can be expressed in the form W = Uhp, where U is a word in .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 509 - 516
Copyright
Copyright © Canadian Mathematical Society 1964

References

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