Geometric Group Theory pp 121-168 | Cite as

# Solution of the Conjugacy Problem and Malnormality of Subgroups in Certain Relative Small Cancellation Group Presentations

## Abstract

The three fundamental decision problems posed by Max Dehn in 1912 are the word problem, the conjugacy problem and the isomorphism problem. Let *G* be a group and let *u* and *v* be elements of *G*. The word problem asks for an algorithm for deciding whether *u* = *v*. The conjugacy problem asks about the existence of an element *g* ∈ *G* which conjugates *u* to *v*, i.e., *v* = *g* ^{−1} *ug*. A solution of the conjugacy problem clearly contains a solution of the word problem. The isomorphism problem asks whether two group presentations define isomorphic groups. The word and conjugacy problems received much attention in the literature. For a summary of results concerning the conjugacy problem until 1987 see [13] and references therein.

## Keywords

Word Problem Free Product Conjugacy Problem Simple Closed Curve Boundary Cycle## Preview

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