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

Author(s)

Goncalves, Daciberg Lima ^[1] ; Guaschi, John ^[2]

Affiliation

^[1] Univ Sao Paulo, IME, Dept Matemat, BR-05314970 Sao Paulo - Brazil

^[2] Univ Caen, CNRS, Lab Math Nicolas Oresme, UMR 6139, F-14032 Caen - France

• Document type: Journal article
• Source: Journal of Group Theory; v. 13, n. 2, p. 277-294, MAR 2010.
• Web of Science Citations: 5

Abstract

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). (AU)

• FAPESP's process: 04/10229-6 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants