= Piece in small cancellation theory
= Small cancellation piece
{synonym}
A piece is a nontrivial combinatorial path that occurs in two essentially distinct positions on oriented cell attaching paths. These may be different cells or distinct admissible occurrences on one attaching path; occurrences identified by the defining attaching-path symmetry are not counted twice. In a symmetrized <group presentation>, it is a common initial segment of distinct <relator> words. Internal arcs of a <reduced disc diagram> are pieces, because otherwise the neighboring cells form a cancellable pair.
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