Irreducible Subgroups of Exceptional Algebraic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Irreducible Subgroups of Exceptional Algebraic Groups write by Donna M. Testerman. This book was released on 1988. Irreducible Subgroups of Exceptional Algebraic Groups available in PDF, EPUB and Kindle. Let [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on some rational [italic]k[italic]Y module [italic]V. This extends work of Dynkin who obtained a similar classification for algebraically closed fields of characteristic 0. The main result has been combined with work of G. Seitz to obtain a classification of the maximal closed connected subgroups of the classical algebraic groups defined over [italic]k.
The Irreducible Subgroups of Exceptional Algebraic Groups
The Irreducible Subgroups of Exceptional Algebraic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Irreducible Subgroups of Exceptional Algebraic Groups write by Adam R. Thomas. This book was released on 2021-06-18. The Irreducible Subgroups of Exceptional Algebraic Groups available in PDF, EPUB and Kindle. This paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.
Irreducible Subgroups of Exceptional Algebraic Groups
Irreducible Subgroups of Exceptional Algebraic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Irreducible Subgroups of Exceptional Algebraic Groups write by Adam Robert Thomas. This book was released on 2014. Irreducible Subgroups of Exceptional Algebraic Groups available in PDF, EPUB and Kindle.
Maximal Subgroups of Exceptional Algebraic Groups
Maximal Subgroups of Exceptional Algebraic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximal Subgroups of Exceptional Algebraic Groups write by Gary M. Seitz. This book was released on 1991. Maximal Subgroups of Exceptional Algebraic Groups available in PDF, EPUB and Kindle. Let [italic]G be a simple algebraic group of exceptional type over an algebraically closed field of characteristic [italic]p. The subgroups of [italic]G maximal with respect to being closed and connected are determined, although mild restrictions on [italic]p are required in dealing with certain simple subgroups of low rank. For [italic]p = 0 we recover the results of Dynkin.
On Non-Generic Finite Subgroups of Exceptional Algebraic Groups
On Non-Generic Finite Subgroups of Exceptional Algebraic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Non-Generic Finite Subgroups of Exceptional Algebraic Groups write by Alastair J. Litterick. This book was released on 2018-05-29. On Non-Generic Finite Subgroups of Exceptional Algebraic Groups available in PDF, EPUB and Kindle. The study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.
