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Free Linear Actions of Finite Groups on Products of Two Spheres

โœ Scribed by U. Ray


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
377 KB
Volume
162
Category
Article
ISSN
0021-8693

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๐Ÿ“œ SIMILAR VOLUMES


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We find a necessary and sufficient condition for an amalgamated free product of arbitrarily many isomorphic residually \(p\)-finite groups to be residually \(p\)-finite. We also prove that this condition is sufficient for a free product of any finite number of residually \(p\)-finite groups, amalgam

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We prove that the analog of the Grushko-Neumann theorem does not hold for profinite free products of profinite groups. To do that we bound the number of generators of a finite group generated by a family of subgroups of pairwise coprime orders.

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A subset of a group is said to be product-free if the product of two of its elements is never itself an element of the subset. Using the classification of finite simple groups, we prove that every finite group of order n has a product-free subset of more than cn 11ร‚14 elements, for some fixed c>0. T

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We derive necessary and sufficient conditions for generalized free products of free groups or finitely generated torsion-free nilpotent groups, amalgamating a cycle, to be residually finite p-groups. Using this, we characterize the residually finite p-group property of tree products of finitely gene