THE SEMIPRIMITIVITY PROBLEM FOR GROUP-ALGEBRAS OF LOCALLY FINITE-GROUPS

Authors
Citation
Ds. Passman, THE SEMIPRIMITIVITY PROBLEM FOR GROUP-ALGEBRAS OF LOCALLY FINITE-GROUPS, Israel Journal of Mathematics, 96, 1996, pp. 481-509
Citations number
22
Categorie Soggetti
Mathematics, General",Mathematics
ISSN journal
00212172
Volume
96
Year of publication
1996
Part
B
Pages
481 - 509
Database
ISI
SICI code
0021-2172(1996)96:<481:TSPFGO>2.0.ZU;2-1
Abstract
Let K[G] be the group algebra of a locally finite group G over a held K of characteristic p > 0. If G has a locally subnormal subgroup of or der divisible by p, then it is easy to see that the Jacobson radical J K[G] is not zero. Here, we come close to a complete converse by showin g that if G has no nonidentity locally subnormal subgroups, then K[G] is semiprimitive. The proof of this theorem uses the much earlier semi primitivity results on locally finite, locally p-solvable groups, and the more recent results on locally finite, infinite simple groups. In addition, it uses the beautiful properties of finitary permutation gro ups.