Chapter 2. Free Groups

By Bergman, G. M.

Book Id: WPLBN0000667876
Format Type: PDF eBook
File Size: 114.53 KB
Reproduction Date: 2005

Title:	Chapter 2. Free Groups
Author:	Bergman, G. M.
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Bergman, G. (n.d.). Chapter 2. Free Groups. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: In this chapter, we introduce the idea of universal constructions through the particular case of free groups. We shall first motivate the free group concept, then develop three ways of constructing such groups. 2.1. Motivation. Suppose G is a group and we take (say) three elements a, b, cE|G|, and consider what group-theoretic relations these satisfy. That is, letting T be the set of all group theoretic terms in three symbols x, y and z, we look at pairs of elements p(x, y, z), q(x, y, z) ET, and if pG(a, b, c) = qG(a, b, c) in |G|, we say that (a, b, c) satisfies the relation p = q. We note...