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A uniqueness lemma for groups generated by 3-transpositions

  • Richard Weiss (a1)
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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

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[2]Blass, A.. Graphs with unique maximal clumpings. J. Graph. Theory 2 (1978), 1924.
[3]Danielson, S., Guterman, M. and Weiss, R.. On Fischer's characterizations of Σ5 and Σn. Comm. Algebra 11 (1983), 15011510.
[4]Fischer, B.. Finite groups generated by 3-transpositions. Invent. Math. 13 (1971), 232246, and University of Warwick Lecture Notes. (Unpublished.)
[5]Griess, B.. The friendly giant. Invent. Math. 69 (1982), 1102.
[6]Parrott, D.. Characterizations of the Fischer groups I, II, III. Trans. Amer. Math. Soc. 265 (1981), 303347.
[7]Weiss, B.. On Fischer's characterization of Spεn(2) and Un(2). Comm. Algebra 11 (1983), 25272554.
[8]Weiss, R.. 3-transpositions in infinite groups. Math. Proc. Cambridge Philos. Soc. 96 (1984), 371377.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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