Decomposing p-groups via Jordan algebras

JOURNAL OF ALGEBRA

卷:322

Article

Wilson, James B.

关键词: Central product;    Bilinear maps;    p-Groups;    Jordan algebras;   

DOI  :  10.1016/j.jalgebra.2009.07.029

来源: Elsevier

【 摘 要 】

For finite p-groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P: the number of members in the decomposition, the multiset of orders of the members, and the multiset of orders of their centers. Unlike for direct product decompositions, Aut P is not always transitive on the set of fully refined central decompositions, and the number of orbits can in fact be any positive integer. The proofs use the standard semi-simple and radical structure of Jordan rings. These rings also produce useful criteria for a p-group to be centrally indecomposable. Applications to p-groups of class 2 and arbitrary exponent are also provided. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free