(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 2, PAGES 115-125

## On relatively aspherical presentations and their central extensions

O. V. Kulikova

Abstract

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Under the condition of asphericity of a quotient group $G/\bar N$R, mutual commutants of the form $\left[\bar N$R,G] in hyperbolic groups $G$ are investigated together with the structure of central subgroups $\bar N$R/[\bar NR, G] in central extensions $G/\left[\bar N$R, G] of $G/\bar N$R. In particular, quotients of the form $G/\left[gm,G\right]$ are considered, where $g$ is an element of infinite order from a hyperbolic group $G$ and $m$ is sufficiently large (depending on $g$).

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