A class of special p-groups
- 98 Downloads
Starting by the multiplication table of a finite group G, for each odd prime p a special p-group P of exponent p is constructed. Some connections between the structures of G and P, concerning subgroups and automorphisms, are given. When p does not divide the order of G, for every normal subgroup of G a direct decomposition of P is done. Besides, the order of the derived subgroup of G is proved to be connected with the existence of some abelian subgroups of maximal order in P. Finally, the elements of P with large centralizers are characterized in terms of algebraic properties of the multiplication table of G.
KeywordsNormal Subgroup Finite Group Abelian Subgroup Maximal Order Permutation Matrix
Unable to display preview. Download preview PDF.