Extremal and maximal normal abelian subgroups of a maximal unipotent subgroup in groups of Lie type
Copyright policy )Extremal and maximal normal abelian subgroups of a maximal unipotent subgroup in groups of Lie type
Let \(G\) be a group of Lie type over a field \(K\) and let \(U\) be the unipotent radical of a Borel subgroup of \(G\). The authors, [\textit{V.~M. Levchuk} and \textit{G.~S. Suleimanova}, Dokl. Math. 77, No. 2, 284-287 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 419, No. 5, 595-598 (2008; Zbl 1156.20037)], describe all maximal Abelian normal subgroups of \(U\) when \(G\) is of classical type. In the present paper they complete the description for the remaining types (the descriptions are too complicated to give here). In particular, they give an alternative solution to the problem of classifying normal Abelian subgroups of \(U\) with simple corners which was considered by \textit{C. Parker} and \textit{P. Rowley} in a series of papers [culminating in Commun. Algebra 31, No. 7, 3471-3486 (2003; Zbl 1034.20043)]. In the case where \(K\) is finite the authors give a complete list of the normal Abelian subgroups of maximum order in \(U\) (Theorem 6.1); in particular, they conclude that the largest normal Abelian subgroups of \(U\) have the same size as the largest Abelian subgroups (Theorem 6.4).
- Siberian Federal University Russian Federation
Algebra and Number Theory, extremal subgroups, maximal Abelian normal subgroups, Subgroup theorems; subgroup growth, Other matrix groups over fields, Maximal abelian normal subgroup, Group of Lie type, Linear algebraic groups over arbitrary fields, Large abelian subgroup, Unipotent subgroup, Special subgroups (Frattini, Fitting, etc.), Maximal subgroups, Extremal subgroup, Simple groups: alternating groups and groups of Lie type, unipotent subgroups, large Abelian subgroups, groups of Lie type
Algebra and Number Theory, extremal subgroups, maximal Abelian normal subgroups, Subgroup theorems; subgroup growth, Other matrix groups over fields, Maximal abelian normal subgroup, Group of Lie type, Linear algebraic groups over arbitrary fields, Large abelian subgroup, Unipotent subgroup, Special subgroups (Frattini, Fitting, etc.), Maximal subgroups, Extremal subgroup, Simple groups: alternating groups and groups of Lie type, unipotent subgroups, large Abelian subgroups, groups of Lie type
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!