Groups which act freely onRm×Sn−1

Constructing free actions ofp–groups on products of spheres

“…In Section 2 we first prove that, for all integers k 0, there exists a positive integer q such that the group k .Aut G .S.V˚q/// is finite. We then incorporate this result in an outline of a known construction (see Adem [3], Connolly and Prassidis [8] and Ilhan [15]) that, in favourable conditions, gives a strategy to build group actions on products of spheres with controlled isotropy subgroups.…”

“…The motivation comes from a result of Connolly and Prassidis [8] stating that a group with finite virtual cohomological dimension that is countable and with rank 1 finite subgroups acts freely on a finite dimensional CW-complex X ' S m . We show that an effective -sphere does not need to exist but that the algebraic analogue still holds.…”

Constructing homologically trivial actions on products of spheres

“…In different forms, this proposition also appears in [4], [12], and [18]. Here we give a proof of it for completeness since it is the main ingredient in the proof of Theorem 1.2.…”

“…For more details on this material we refer the reader to [13] and [22]. Some of this material also appears in [4], [9], [12], and [18]. Definition 2.1.…”

“…Using this method, after some steps, one gets a free action on a product of spheres. This method was first developed by Connolly and Prassidis [4] and later used also in [2] and [18].…”