Journal of Lie Theory 17 (2007), No. 3, 625--632
Copyright Heldermann Verlag 2007
On Compact Just-Non-Lie Groups
Dip. di Matematica, UniversitÓ di Napoli, Via Cinthia, 80126 Naples, Italy
A compact group is called a compact Just-Non-Lie group or a compact JNL group if it is not a Lie group but all of its proper Hausdorff quotient groups are Lie groups. We show that a compact JNL group is profinite and a compact nilpotent JNL group is the additive group of p-adic integers for some prime. Examples show that this fails for compact pronilpotent and solvable groups.
Keywords: Compact just-non-Lie groups, centerfree compact groups.
MSC: 22C05, 20E22, 20E34
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