Arbitrary groups as two-point stabilisers of symmetric groups acting on partitions
J.P. James
Department for Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK
DOI: 10.1007/s10801-006-0034-3
Abstract
We give a short, direct proof that given any finite group G there exist positive integers k and l and partitions α 1and α 2 of {1, \cdots , kl } into l subsets of size k such that ( S kl ) α 1, α 2\cong G.
The method used will also show that given any finite group G there exists a regular bipartite graph whose automorphism group is isomorphic to G
Pages: 355–360
Keywords: keywords symmetric groups acting on partitions; regular bipartite graphs; two-point stabilisers
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References
1. J.P. James, “Partition actions of symmetric groups and regular bipartite graphs,” Bulletin of the London Mathematical Society 38 (2006), 224-232.
2. J.P. James, PhD thesis, The University of Cambridge, (2006). In preparation.
3. W.M. Kantor, “Automorphisms and isomorphisms of symmetric and affine designs,” Journal of Algebraic Combinatorics 3 (1994), 307-338.
2. J.P. James, PhD thesis, The University of Cambridge, (2006). In preparation.
3. W.M. Kantor, “Automorphisms and isomorphisms of symmetric and affine designs,” Journal of Algebraic Combinatorics 3 (1994), 307-338.
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