Isomorphisms of modular group algebras: An algorithm and its application to groups of order 26

✍ Scribed by Martin Wursthorn

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 445 KB
• Volume: 15
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1993.1015

✦ Synopsis

We shall describe an algorithm based on an idea of Roggenkamp and Scott (Roggenkamp and Scott, 1993) ) to compute (\mathrm{Hom}_{\text {alg }}(\mathbb{F} H, \mathbb{F} G) ), where (H, G) are finite (p)-groups and (\mathbb{F} H, \mathbb{F} G) are their group algebras over (\mathbb{F}=\mathbb{Z} / p \mathbb{Z}). Using this algorithm it is possible to determine whether two such group algebras are isomorphic. An implementation of the algorithm has been used to show that the groups of order 64 are determined by their modular group algebras over (\mathbb{Z} / 2 \mathbb{Z}).