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)
Famous quotes containing the words normal and/or forms:
“Normality highly values its normal man. It educates children to lose themselves and to become absurd, and thus to be normal. Normal men have killed perhaps 100,000,000 of their fellow normal men in the last fifty years.”
—R.D. (Ronald David)
“The atmosphere of orthodoxy is always damaging to prose, and above all it is completely ruinous to the novel, the most anarchical of all forms of literature.”
—George Orwell (1903–1950)