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3-transpositions in infinite groups

Published online by Cambridge University Press:  24 October 2008

Richard Weiss
Richard Weiss
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, U.S.A.
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Let G be a group. A subset D will be called a set of 3-transpositions if |x| = 2 for xεD and |xy| = 3 whenever x, yεD do not commute. We will call the set D closed if xDx−1 = D for each xεD. For each xεD, let

For each subset X of D, we denote by [X] the graph with vertex set X where two elements x, yεX are joined by an edge whenever they commute. We denote by (X) the complement graph; thus two elements x, yεX are joined by an edge of (X) whenever they do not commute.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 3 , November 1984 , pp. 371 - 377
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Aschbacher, M.. A homomorphism theorem for finite graphs. Proc. Amer. Math. Soc. 54 (1976), 468–470.CrossRefGoogle Scholar
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[3]Fischer, B.. Finite groups generated by 3-transpositions. Invent. Math. 13 (1971), 232–246 and University of Warwick Lecture Notes (unpublished).Google Scholar