A general measuring argument for finite permutation groups

Goren, Avi; Herzog, Marcel

doi:10.1090/S0002-9939-09-09993-6

A general measuring argument for finite permutation groups
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by Avi Goren and Marcel Herzog PDF

Proc. Amer. Math. Soc. 137 (2009), 3197-3205 Request permission

Abstract:

In Chermak and Delgado’s paper “A measuring argument for finite groups”, a certain “measuring lemma” was shown to hold. This lemma has been successfully applied in many recent papers. We generalize this lemma by expanding the discussion from groups acting on groups to groups acting on sets. As applications, we obtain the main results of several earlier papers.

References

Andrew Chermak and Alberto Delgado, A measuring argument for finite groups, Proc. Amer. Math. Soc. 107 (1989), no. 4, 907–914. MR 994774, DOI 10.1090/S0002-9939-1989-0994774-4
Andrew Chermak and Alberto L. Delgado, $J$-modules for local $BN$-pairs, Proc. London Math. Soc. (3) 63 (1991), no. 1, 69–112. MR 1105719, DOI 10.1112/plms/s3-63.1.69
George Glauberman, Centrally large subgroups of finite $p$-groups, J. Algebra 300 (2006), no. 2, 480–508. MR 2228208, DOI 10.1016/j.jalgebra.2005.11.033
George Glauberman, Large subgroups of small class in finite $p$-groups, J. Algebra 272 (2004), no. 1, 128–153. MR 2029028, DOI 10.1016/j.jalgebra.2002.11.003
Avi Goren, A measuring argument for finite permutation groups, Israel J. Math. 145 (2005), 333–339. MR 2154734, DOI 10.1007/BF02786698
Avi Goren, Another measuring argument for finite permutation groups, J. Group Theory 10 (2007), no. 6, 829–840. MR 2364831, DOI 10.1515/JGT.2007.061
Robert Guralnick and Gerhard Röhrle, Weakly closed unipotent subgroups in Chevalley groups, J. Algebra 300 (2006), no. 2, 729–740. MR 2228219, DOI 10.1016/j.jalgebra.2005.12.015
I. M. Isaacs, Abelian point stabilizers in transitive permutation groups, Proc. Amer. Math. Soc. 130 (2002), no. 7, 1923–1925. MR 1896023, DOI 10.1090/S0002-9939-01-06400-0
Andrea Lucchini, On the order of transitive permutation groups with cyclic point-stabilizer, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 9 (1998), no. 4, 241–243 (1999) (English, with English and Italian summaries). MR 1722784