Bender's method

In group theory, Bender's method is a method introduced by Bender (1970) for simplifying the local group theoretic analysis of the odd order theorem. Shortly afterwards he used it to simplify Walter's analysis of groups with abelian Sylow 2-subgroups, and Gorenstein and Walter's classification of groups with dihedral Sylow 2-subgroups. Bender's method involves studying a maximal subgroup M containing the centralizer of an involution, and its generalized Fitting subgroup F^*(M).

References

• Bender, Helmut (1970), "On the uniqueness theorem", Illinois Journal of Mathematics, 14: 376–384, ISSN 0019-2082, MR0262351
• Bender, Helmut (1970b), "On groups with abelian Sylow 2-subgroups", Mathematische Zeitschrift, 117: 164–176, doi:10.1007/BF01109839, ISSN 0025-5874, MR0288180
• Bender, Helmut; Glauberman, George (1994), Local analysis for the odd order theorem, London Mathematical Society Lecture Note Series, vol. 188, Cambridge University Press, ISBN 978-0-521-45716-3, MR1311244
• Gagen, Terence M. (1976), Topics in finite groups, Cambridge University Press, ISBN 978-0-521-21002-7, MR0407127