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A uniqueness lemma for groups generated by 3-transpositions

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 of G will be called a set of 3-transpositions if |x| =2 for all xεD and |xy| = 3 whenever x, yεD do not commute. We will call the set D closed if xDx = D for each xεD. For each xεD, let

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 421 - 431
Copyright
Copyright © Cambridge Philosophical Society 1985

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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
[2]Blass, A.. Graphs with unique maximal clumpings. J. Graph. Theory 2 (1978), 19–24.CrossRefGoogle Scholar
[3]Danielson, S., Guterman, M. and Weiss, R.. On Fischer's characterizations of Σ5 and Σn. Comm. Algebra 11 (1983), 1501–1510.CrossRefGoogle Scholar
[4]Fischer, B.. Finite groups generated by 3-transpositions. Invent. Math. 13 (1971), 232–246, and University of Warwick Lecture Notes. (Unpublished.)CrossRefGoogle Scholar
[5]Griess, B.. The friendly giant. Invent. Math. 69 (1982), 1–102.CrossRefGoogle Scholar
[6]Parrott, D.. Characterizations of the Fischer groups I, II, III. Trans. Amer. Math. Soc. 265 (1981), 303–347.CrossRefGoogle Scholar
[7]Weiss, B.. On Fischer's characterization of Spεn(2) and Un(2). Comm. Algebra 11 (1983), 2527–2554.CrossRefGoogle Scholar
[8]Weiss, R.. 3-transpositions in infinite groups. Math. Proc. Cambridge Philos. Soc. 96 (1984), 371–377.CrossRefGoogle Scholar