The modular isomorphism problem for finite $p$-groups with a cyclic subgroup of index $p^2$
| dc.creator | Bagiński, Czesław | |
| dc.creator | Konovalov, Alexander | |
| dc.date | 2006-07-12 | |
| dc.date.accessioned | 2026-07-07T08:08:02Z | |
| dc.date.available | 2026-07-07T08:08:02Z | |
| dc.description | Let $p$ be a prime number, $G$ be a finite $p$-group and $K$ be a field of characteristic $p$. The Modular Isomorphism Problem (MIP) asks whether the group algebra $KG$ determines the group $G$. Dealing with MIP, we investigated a question whether the nilpotency class of a finite $p$-group is determined by its modular group algebra over the field of $p$ elements. We give a positive answer to this question provided one of the following conditions holds: (i) $\exp G=p$; (ii) $\cl(G)=2$; (iii) $G'$ is cyclic; (iv) $G$ is a group of maximal class and contains an abelian subgroup of index $p$. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0607292 | |
| dc.identifier | http://arxiv.org/abs/math/0607292 | |
| dc.identifier | Groups St Andrews 2005. Vol.I, volume 339 of London Math. Soc. Lecture Note Ser., p.186-193. Cambridge Univ. Press, Cambridge, 2007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131124 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Group Theory | |
| dc.subject | 16S34, 20C05 | |
| dc.title | The modular isomorphism problem for finite $p$-groups with a cyclic subgroup of index $p^2$ | |
| dc.type | text |