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A homotopy type of a p–group with cyclic centre

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

S. B. Conlon
S. B. Conlon
Affiliation:
Department of Pure MathematicsUniversity of SydneySydney, N.S.W. 2006, Australia
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Abstract

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Let G be a p–group with cyclic L(G) = Z. Then L(G) = {Z < H ≦ G|H′ ∩ Z = (1)}, a poset ordered under inclusion. Then the associated simplicial complex |L(G)| is homotopic to a bouquet of spheres. A subgroup E of G is called a CES if CG (E) = Z = L(E) and if E/Z is elementary. Then |L(G)| is homotopic to the one-point union of the |L(E)| for all CES's E in G. If |E/Z| = p2n then |L(E)| is homotopic to a one-point union of pn2 (n– 1)-spheres.

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 1 , August 1985 , pp. 94 - 100
Copyright
Copyright © Australian Mathematical Society 1985

References

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