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A practical method for enumerating cosets of a finite abstract group

Published online by Cambridge University Press:  20 January 2009

J. A. Todd  and
H. S. M. Coxeter
J. A. Todd
Affiliation:
(University of Manchester)
H. S. M. Coxeter
Affiliation:
(University of Cambridge).
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An important problem in finite-group theory is the determination of an abstract definition for a given group , that is, a set of relations

between k generating operations S1, …., Sk of , such that every other relation between S1, …., Sk is an algebraic consequence of (1).

The number of groups for which abstract definitions are actually known is relatively small, but a remarkable feature of the results already obtained is the extreme simplicity of the relations (1) in the case of several groups of quite high order. This fact constitutes an additional incentive to the search for abstract definitions, and many elegant results have doubtless yet to be discovered.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 5 , Issue 1 , October 1936 , pp. 26 - 34
Copyright
Copyright © Edinburgh Mathematical Society 1936

References

page 27 note 1 See, e.g., Moore, , Proc. London Math. Soc. (1), 28 (1897) 357–366;Google ScholarDickson, , Linear Groups (Leipzig, 1901).Google Scholar

page 28 note 1 See, e.g., Burnside, , Theory of Groups, 2nd Ed. (Cambridge, 1911), Ch. XII.Google Scholar

page 29 note 1 We use this word by analogy with the case of a set of homogeneous linear equations whose only solution is the trivial one: 0, 0,......, 0.

page 33 note 1 Todd, , Proc. Camb. Phil. Soc., 27 (1931), 221.Google Scholar