Groups St Andrews 2001 in Oxford: Volume 2 by C. M. Campbell, E. F. Robertson, G. C. Smith

By C. M. Campbell, E. F. Robertson, G. C. Smith

This two-volume set includes chosen papers from the convention teams St. Andrews 2001 in Oxford. Contributed through best researchers, the articles disguise a large spectrum of recent crew idea. Contributions in keeping with lecture classes given via 5 major audio system are incorporated with refereed survey and examine articles. The teams St. Andrews lawsuits volumes symbolize a view of the state-of-the-art in crew conception and sometimes play an enormous position in destiny advancements within the topic.

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Thesis, University of Wisconsin, Madison, 1973. [31] D. Gluck, Trivial set stabilizers in finite permutation groups, Canad. J. Math. 35 (1983), 59–67. [32] D. Gluck, On the k(GV )–problem, J. Algebra 89 (1984), 46–55. [33] D. Gluck, Bounding the number of character degrees of a solvable group, J. London Math. Soc. (2) 31 (1985), 457–462. [34] D. Gluck, K. Magaard, Base sizes and regular orbits for coprime affine permutation groups, J. London Math. Soc. 58 (1998), 603–618. [35] D. Gluck, K. Magaard, The extraspecial case of the k(GV )–problem, Trans.

6] T. R. Berger, B. B. Hargraves, C. Shelton, The regular module problem II, Comm. Algebra 18 (1990), 74–91. [7] T. R. Berger, B. B. Hargraves, C. Shelton, The regular module problem III, J. Algebra 131 (1990), 74–91. [8] R. Brauer, Number theoretical investigations on groups of finite order, Proceedings of the International Symposium on Algebraic Number Theory, Tokyo, (1956), 55–62. [9] R. Brauer, W. Feit, On the number of irreducible characters of finite groups in a given block, Proc. Nut. Acad.

6 Orbits of permutation groups on the power set In this last section we are concerned with permutation groups on a finite set Ω and their action on P(Ω), the power set of Ω. Note that if for A, B ∈ P(Ω) we define A + B := (A ∪ B) − (A ∩ B) = (A − B) ∪ (B − A), 324 KELLER then P(Ω) with this addition becomes a GF (2)–module, and thus the action of G on P(Ω) fits within the framework of this article of studying linear group actions, and as we will see, it has raised some interest and found important applications in the past, some of which are related to the previously discussed topics.

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