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MAXIMAL SUBGROUPS OF SOME NON LOCALLY FINITE p-GROUPS.
- Source :
-
International Journal of Algebra & Computation . Oct/Dec2005, Vol. 15 Issue 5/6, p1129-1150. 22p. - Publication Year :
- 2005
-
Abstract
- Kaplansky's conjecture claims that the Jacobson radical $\mathcal{J}K[G]$ of a group algebra K[G], where K is a field of characteristic p > 0, coincides with its augmentation ideal $\mathcal{A}K[G]$ if and only if G is a locally finite p-group. By a theorem of Passman, if G is finitely generated and $\mathcal{J}K[G]=\mathcal{A}K[G]$ then any maximal subgroup of G is normal of index p. In the present paper, we consider one infinite series of finitely generated infinite p-groups (hence not locally finite p-groups), so called GGS-groups. We prove that their maximal subgroups are nonetheless normal of index p. Thus these groups remain among potential counterexamples to Kaplansky's conjecture. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181967
- Volume :
- 15
- Issue :
- 5/6
- Database :
- Academic Search Index
- Journal :
- International Journal of Algebra & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 19318695
- Full Text :
- https://doi.org/10.1142/S0218196705002803