We compute the group homology, the topological K–theory of the reduced C∗– algebra, the algebraic K–theory and the algebraic L–theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1 → K → G → Q → 1 of a torsionfree grou...

We compute the group homology, the topological K–theory of the reduced C∗– algebra, the algebraic K–theory and the algebraic L–theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1 → K → G → Q → 1 of a torsionfree grou...

There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on top. The in shuffle I leaves the original top card second from the top. Applications to the design of computer networks and card tricks are reviewed. The main result is the determination of the group (I, 0) generated by the two ...