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

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 >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

International Cooperation USP/COFECUB

International Cooperation USP/COFECUB[105/06]

Universite Paul Sabatier

Universite Paul Sabatier

Pro-Reitoria de Pesquisa Projeto 1

Pro-Reitoria de Pesquisa Projeto 1

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Projeto Tematico FAPESP[2004/10229-6]