Generation in Groups

Ernest Shult () and David Surowski
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Ernest Shult: Kansas State University, Department of Mathematics

Chapter Chapter 6 in Algebra, 2015, pp 163-184 from Springer

Abstract: Abstract Here, the free group on set X is defined to be the automorphism group of a certain tree with labeled edge-directions. This approach evades some awkwardness in dealing with reduced words. The universal property that any group generated by a set of elements X is a homomorphic image of the free group on X, as well as the fact that a subgroup of a free group is free (possibly on many more generators) are easy consequences of this definition. The chapter concludes with a discussion of (k, l, m)-groups and the Brauer-Ree theorem.

Keywords: Directed Edge; Free Radicals; Cayley Graph; Ingoing Edge; Finite Simple Groups (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-19734-0_6

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