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Connectivity of the coset poset and the subgroup poset of a group
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Daniel A. Ramras
Published/Copyright:
November 18, 2005
Abstract
We study the connectivity of the coset poset and the subgroup poset of a group, focusing in particular on simple connectivity. The coset poset was recently introduced by K. S. Brown in connection with the probabilistic zeta function of a group. We take Brown’s study of the homotopy type of the coset poset further, and in particular generalize his results on direct products and classify direct products with simply connected coset posets.
The homotopy type of the subgroup poset L(G ) has been examined previously by Kratzer, Thévenaz, and Shareshian. We generalize some results of Kratzer and Thévenaz, and determine π1(L(G )) in nearly all cases.
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Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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Articles in the same Issue
- Elements of order at most 4 in finite 2-groups, 2
- On the number of infinite branches in the graph of all p-groups of coclass r
- Polynomial properties in unitriangular matrices. II
- Connectivity of the coset poset and the subgroup poset of a group
- The number of non-solutions of an equation in a group
- Groups, periodic planes and hyperbolic buildings
- Endomorphisms preserving an orbit in a relatively free metabelian group
- Generic units in abelian group rings
- Subgroup growth of Baumslag–Solitar groups
