Free actions of finite groups on Sn × Sn
Transactions of the American Mathematical Society
3289 - 3317
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Let p be an odd prime. We construct a non-abelian extension G of S 1 by Z/p × Z/p, and prove that any finite subgroup of G acts freely and smoothly on S2p-1 × S2p-1. In particular, for each odd prime p we obtain free smooth actions of infinitely many non-metacyclic rank two p-groups on S2p-1 × S2p-1. These results arise from a general approach to the existence problem for finite group actions on products of equidimensional spheres.