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A First Step Toward the Classification of Fischer Groups

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Abstract

If G is a finite group, a subset D of G Is called a “Fischer set” of G (or a set of “3-transpositions of G”) if the following conditions are satisfied:

  1. (1)

    G = < D >;

  2. (2)

    each element of D is an involution;

  3. (3)

    if d and e are two distinct elements of D, then de is of order 2 or 3;

  4. (4)

    D is an union of conjugacy classes of G.

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Bibliography

  1. B. FISCHER Finite Groups generated by 3-transpositions.Preprint, University of Warwick (1969).

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© 1988 D. Reidel Publishing Company, Dordrecht, Holland

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Zara, F. (1988). A First Step Toward the Classification of Fischer Groups. In: Aschbacher, M., Cohen, A.M., Kantor, W.M. (eds) Geometries and Groups. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4017-8_18

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  • DOI: https://doi.org/10.1007/978-94-009-4017-8_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8282-2

  • Online ISBN: 978-94-009-4017-8

  • eBook Packages: Springer Book Archive

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