Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

Details Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

2007-10-31

arxiv.org/abs/0710.5940v1

Journal of Group Theory 13, 2 (2010) 277-294

Mathematics

Group Theory

15 pages

Scientific paper

We classify the (finite and infinite) virtually cyclic subgroups of the pure braid groups $P_{n}(RP^2)$ of the projective plane. The maximal finite subgroups of $P_{n}(RP^2)$ are isomorphic to the quaternion group of order 8 if $n=3$, and to $\Z_{4}$ if $n\geq 4$. Further, for all $n\geq 3$, up to isomorphism, the following groups are the infinite virtually cyclic subgroups of $P_{n}(RP^2)$: $\Z$, $\Z_{2} \times \Z$ and the amalgamated product $\Z_{4} \ast_{\Z_{2}} \Z_{4}$.

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