ISOMORPHISMS OF PARTIAL GROUP RINGS

Author(s)

Dokuchaev, M. ^[1] ; Simon, J. ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Matemat, Caixa Postal 66-281, BR-05315970 Sao Paulo - Brazil

^[2] Univ Murcia, Dept Matemat, Murcia - Spain

• Document type: Journal article
• Source: COMMUNICATIONS IN ALGEBRA; v. 44, n. 2, p. 680-696, 2016.
• Web of Science Citations: 3

Abstract

We prove that if two finite groups G(1) and G(2) admit an isomorphism between their lattices of subgroups which preserves subgroup rings over a commutative ring K then the partial group rings K-par G(1) and K-par G(2) are isomorphic. If vertical bar G vertical bar is odd, then we find a series of natural invariants of C-par G and use them to show that C-par G determines the commutativity of G. In the case of odd vertical bar G vertical bar, the least counterexample to the isomorphism problem for partial group algebras over C is pointed out. Moreover, a counterexample to the isomorphism problem over Q is also given. (AU)

• FAPESP's process: 09/52665-0 - Groups, rings and algebras: interactions and applications
• Grantee: Francisco Cesar Polcino Milies
• Support type: Research Projects - Thematic Grants