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I want to find a comprehensive reference on general linear groups, which has depth discussion about its subgroups (like solvable subgroups, Abelian subgroups, and so on). Can anyone help me with this? Thanks a lot.

edited Oct 7 2011 at 21:06

quid
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asked Oct 7 2011 at 15:35

Student
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The question looks too broad, since all sorts of finite and linear algebraic groups show up as subgroups of general linear groups. So the internal structure of the big group gets arbitrarily complicated. The choice of field also matters a lot, especially if you study general linear groups as targets of representations of smaller groups. There really isn't a comprehensive reference for all of this, especially the representation theory aspect. – Jim Humphreys Oct 7 2011 at 19:07

@Jim: Yes, the question is broad in some sense. I want to know as much as is known for subgroups, in particular, the solvable and abelian subgroups of general linear groups to see whether I can use some of the properties for my applications. @ Mark and Sapir: Thank you for excellent references. Both books are very good. However I think the Suprunenko's book contains more of what I want to know than Wehrfritz's. – Student Oct 8 2011 at 15:41

Mark Sapir · Accepted Answer · 2011-10-07 17:05:12Z UTC

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Suprunenko, "Matrix groups", http://www.amazon.com/Matrix-Groups-D-Suprunenko/dp/0821813412/ref=sr_1_10?s=books&ie=UTF8&qid=1318007030&sr=1-10 .

answered Oct 7 2011 at 17:05

Mark Sapir
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Alain Valette · Answer 2 · 2011-10-07 17:24:54Z UTC

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B.A.F. Wehrfritz, "Infinite linear groups", Ergebnisse der Math. Band 76, Springer-Verlag 1973

answered Oct 7 2011 at 17:24

Alain Valette
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Reference for general linear groups

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