The Compressed Word Problem for Groups by Markus Lohrey

Author:Markus Lohrey
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

By Lemma 4.2, we can just speak about the compressed word problem for G, briefly CWP(G).

Before we consider the compressed word problem in specific groups we prove two preservation results. Recall the reducibility relations from Sect. 1.​3.​3.​ By the following simple proposition, the complexity of the compressed word problem is preserved when going to a finitely generated subgroup.

Proposition 4.3.

Assume that H is a finitely generated subgroup of the finitely generated group G. Then .

Proof.

Choose a generating set Γ for G that contains a generating set Σ for H. Then for a word we have w = 1 in H if and only if w = 1 in G. □

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