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Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane
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Daciberg Lima Gonçalves
Published/Copyright:
July 14, 2009
Abstract
We classify the (finite and infinite) virtually cyclic subgroups of the pure braid groups Pn(ℝP2) of the projective plane. The maximal finite subgroups of Pn(ℝP2) are isomorphic to the quaternion group of order 8 if n = 3, and to ℤ4 if n ⩾ 4. Further, for all n ⩾ 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of Pn(ℝP2): ℤ, ℤ2 × ℤ and the amalgamated product ℤ4 ∗ℤ2 ℤ4.
Received: 2007-12-14
Revised: 2009-03-19
Published Online: 2009-07-14
Published in Print: 2010-March
© de Gruyter 2010
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Articles in the same Issue
- Class numbers of group extensions
- Zeros of Brauer characters and the defect zero graph
- On the vanishing prime graph of solvable groups
- Solvability of generalized monomial groups
- Group algebras of torsion groups and Lie nilpotence
- An axiomatic formation that is not a variety
- Minimal odd order automorphism groups
- Finite groups with normally embedded subgroups
- The influence of ℋ-subgroups on the structure of finite groups
- Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane
- On ω-categorical groups and their completions
