Normal Forms
A normal form for a group G with generating set S is a choice of one reduced word in S for each element of G. For example:
- The words 1, i, j, ij are a normal form for the Klein four-group.
- The words 1, r, r2, ..., rn-1, s, sr, ..., srn-1 are a normal form for the dihedral group Dihn.
- The set of reduced words in S are a normal form for the free group over S.
- The set of words of the form xmyn for m,n ∈ Z are a normal form for the direct product of the cyclic groups 〈x〉 and 〈y〉.
Read more about this topic: Word (group Theory)
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