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Published in:
2015 | OriginalPaper | Chapter
14. van Kampen’s Theorem
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Abstract
The notation for this chapter will be as follows: if \(G\) is a group and \(S\subset G\) a subset we will write \(\langle S\rangle \subset G\) or \(\langle s\mid s\in S\rangle \subset G\) for the normal subgroup generated by \(S\), which is the intersection of all normal subgroups in \(G\) containing \(S\). It’s easy to show that \(\langle S\rangle \) coincides with the subgroup generated by all elements of the type \(gsg^{-1}\), for \(s\in S\) and \(g\in G\).