Abstract
Let V(script F signpG) be the group of normalized units of the group algebra script F signpG of a finite nonabelian p-group G over the field script F signp of p elements. Our goal is to investigate the power structure of V(script F signpG), when it has nilpotency class p. As a consequence, we have proved that if G and H are p-groups with cyclic Frattini subgroups and p > 2, then V(script F signpG) is isomorphic to V(script F signpH) if and only if G and H are isomorphic.
Original language | English |
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Pages (from-to) | 261-268 |
Number of pages | 8 |
Journal | Publicationes Mathematicae Debrecen |
Volume | 65 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 2004 |
Externally published | Yes |
Keywords
- Group algebra
- Group of units
- Isomorphism problem
ASJC Scopus subject areas
- General Mathematics