Some Algorithms for Nilpotent Permutation Groups

Some Algorithms for Nilpotent Permutation Groups

(Received) Let G, H and E be subgroups of a nite nilpotent permutation group of degree n. We describe the theory and implementation of an algorithm to compute the normalizer N G (H) in time polynomial in n, and we give a modiied algorithm to determine whether H and E are conjugate under G and, if so, to nd a conjugating element of G. Other algorithms produce the intersection G \ H and the centr...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

Minimal Permutation Representations of Nilpotent Groups

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible size. We study the structure of such representations and show that for certain groups they may be obtained by a greedy construction. In these situations (except when central involutions intervene) all minimal permutation representations have the same set of orbit sizes. Using the same ideas w...

On minimal degrees of faithful quasi-permutation representations of nilpotent groups

By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....

Some Remarks on Nilpotent Groups with Roots

is soluble for every pG.m and every gGG. Similarly we call a group G a Dor-group if the equation (1) (above) is not only soluble, but uniquely soluble. The class of Fur-groups and the class of Dor-groups will be denoted respectively by Em and Dm. Clearly Em~2)Dm. There is a less trivial relationship between these two classes of groups. If we denote by ©(C) the class of groups which occur as hom...