Two are well known, the generalized quaternion group and the dihedral group. One of the remaining two groups is often considered particularly important, since it is an example of a 2-group of maximal ...
Nilpotent groups arise in Galois theory, as well as in the classification of groups. They also appear prominently in the classification of Lie groups. The definition uses the idea of a central series ...
Commutators originated over 100 years ago as a by-product of computing group characters of nonabelian groups. They are now an established and immensely useful tool in all of group theory. Commutators ...