Families of finite groups arising from direct products... - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T17:33:53Z http://mathoverflow.net/feeds/question/51790 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/51790/families-of-finite-groups-arising-from-direct-products Families of finite groups arising from direct products... Guillermo Pineda-Villavicencio 2011-01-11T22:07:36Z 2011-01-11T22:13:34Z <p>I am interested in families of finite groups arising from direct products of other groups. For instance, abelian groups are a simple example of such families (direct products of cyclic groups), but there are more. The family of hamiltonian groups is another such family; a hamiltonian group is a group where all the subgroups are normal, and it can be expressed as the direct product of the quaternion group of order 8, an abelian group of odd order and a group formed only by involutions. Coxeter groups are other examples; they are represented as direct products of irreducible Coxeter groups.</p> <p>Could you point out to any other such families??</p> <p>Thanks in advance, and regards, Guillermo</p> http://mathoverflow.net/questions/51790/families-of-finite-groups-arising-from-direct-products/51791#51791 Answer by Chris Eagle for Families of finite groups arising from direct products... Chris Eagle 2011-01-11T22:13:34Z 2011-01-11T22:13:34Z <p>A finite group is nilpotent iff it is a direct product of \$p\$-groups.</p>