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Examples and Applications of Infinite Permutation Groups

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Book cover Permutation Groups

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 163))

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Abstract

The object of this chapter is to give a selection of examples of infinite permutation groups, and a few of the ways in which permutation groups can be used in a more general context. For example, we give a criterion of Serre for a group to be free which leads to a classic theorem on free groups due to J. Nielson and O. Schreier, and give a construction due to N. D. Gupta and S. Sidki of an infinite p-group which is finitely generated. What makes these constructions manageable is that the underlying set on which the groups act have certain relational structures. The most symmetric of these structures (the ones with the largest automorphism groups) are the homogeneous structures; of these the countable universal graph is an especially interesting and well-studied example.

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  1. Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, KIS 5B6, Canada

    John D. Dixon & Brian Mortimer

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  1. John D. Dixon
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© 1996 Springer Science+Business Media New York

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Dixon, J.D., Mortimer, B. (1996). Examples and Applications of Infinite Permutation Groups. In: Permutation Groups. Graduate Texts in Mathematics, vol 163. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0731-3_9

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  • DOI: https://doi.org/10.1007/978-1-4612-0731-3_9

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