MAXIMAL SUBGROUPS OF SOME NON LOCALLY FINITE p-GROUPS
2005 ◽
Vol 15
(05n06)
◽
pp. 1129-1150
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Keyword(s):
Kaplansky's conjecture claims that the Jacobson radical [Formula: see text] of a group algebra K[G], where K is a field of characteristic p > 0, coincides with its augmentation ideal [Formula: see text] if and only if G is a locally finite p-group. By a theorem of Passman, if G is finitely generated and [Formula: see text] 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.
2011 ◽
Vol 10
(04)
◽
pp. 615-622
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2013 ◽
Vol 12
(08)
◽
pp. 1350044
Keyword(s):
1975 ◽
Vol 16
(1)
◽
pp. 22-28
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Keyword(s):
1995 ◽
Vol 37
(2)
◽
pp. 205-210
◽
Keyword(s):
2017 ◽
Vol 16
(10)
◽
pp. 1750182
1970 ◽
Vol 17
(2)
◽
pp. 165-171
◽
Keyword(s):
Keyword(s):
1990 ◽
Vol 13
(2)
◽
pp. 311-314
Keyword(s):