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Rights statement: First published in Proceedings of the American Mathematical Society in Volume 141, (6), 2013, published by the American Mathematical Society
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Complements of intervals and prefrattini subalgebras of solvable Lie algebras.
AU - Towers, David A.
N1 - First published in Proceedings of the American Mathematical Society in Volume 141, (6), 2013, published by the American Mathematical Society
PY - 2013
Y1 - 2013
N2 - In this paper we study a Lie-theoretic analogue of a generalisation of the prefrattini subgroups introduced by W. Gasch¨utz. The approach follows that of P. Hauck and H. Kurtzweil for groups, by first considering complements in subalgebra intervals. Conjugacy of these subalgebras is established for a large class of solvable Lie algebras.
AB - In this paper we study a Lie-theoretic analogue of a generalisation of the prefrattini subgroups introduced by W. Gasch¨utz. The approach follows that of P. Hauck and H. Kurtzweil for groups, by first considering complements in subalgebra intervals. Conjugacy of these subalgebras is established for a large class of solvable Lie algebras.
KW - Lie algebras
KW - complemented
KW - solvable
KW - Frattini ideal
KW - prefrattini subalgebra
KW - residual.
U2 - 10.1090/S0002-9939-2012-11521-7
DO - 10.1090/S0002-9939-2012-11521-7
M3 - Journal article
VL - 141
SP - 1893
EP - 1901
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 1088-6826
IS - 6
ER -