ON THE RELATIONSHIP BETWEEN THE CLASS OF A LIE ALGEBRA AND THE CLASSES OF ITS SUBALGEBRAS
2008 ◽
Vol 18
(01)
◽
pp. 83-95
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Keyword(s):
A classical nilpotency result considers finite p-groups whose proper subgroups all have class bounded by a fixed number n. We consider the analogous property in nilpotent Lie algebras. In particular, we investigate whether this condition puts a bound on the class of the Lie algebra. Some p-group results and proofs carry over directly to the Lie algebra case, some carry over with modified proofs and some fail. For the final of these cases, a certain metabelian Lie algebra is constructed to show a case when the p-groups and Lie algebra cases differ.
Keyword(s):
2007 ◽
Vol 17
(03)
◽
pp. 527-555
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1999 ◽
Vol 42
(3)
◽
pp. 521-540
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Keyword(s):
2012 ◽
Vol 11
(01)
◽
pp. 1250001
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Keyword(s):
2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
◽
2019 ◽
Vol 19
(01)
◽
pp. 2050012
Keyword(s):
1954 ◽
Vol 64
(2)
◽
pp. 200-208
Keyword(s):