Finite Presentability of S-Arithmetic Groups Compact Presentability of Solvable Groups
Abels, Herbert.
Finite Presentability of S-Arithmetic Groups Compact Presentability of Solvable Groups [electronic resource] / by Herbert Abels. - VI, 182 p. online resource. - Lecture Notes in Mathematics, 1261 0075-8434 ; . - Lecture Notes in Mathematics, 1261 .
Compact presentability and contracting automorphisms -- Filtrations of Lie algebras and groups -- A necessary condition for compact presentability -- Implications of the necessary condition -- The second homology -- S-arithmetic groups -- S-arithmetic solvable groups.
The problem of determining which S-arithmetic groups have a finite presentation is solved for arbitrary linear algebraic groups over finite extension fields of #3. For certain solvable topological groups this problem may be reduced to an analogous problem, that of compact presentability. Most of this monograph deals with this question. The necessary background material and the general framework in which the problem arises are given partly in a detailed account, partly in survey form. In the last two chapters the application to S-arithmetic groups is given: here the reader is assumed to have some background in algebraic and arithmetic group. The book will be of interest to readers working on infinite groups, topological groups, and algebraic and arithmetic groups.
9783540471981
10.1007/BFb0079708 doi
Group theory.
Topological Groups.
Group Theory and Generalizations.
Topological Groups, Lie Groups.
QA174-183
512.2
Finite Presentability of S-Arithmetic Groups Compact Presentability of Solvable Groups [electronic resource] / by Herbert Abels. - VI, 182 p. online resource. - Lecture Notes in Mathematics, 1261 0075-8434 ; . - Lecture Notes in Mathematics, 1261 .
Compact presentability and contracting automorphisms -- Filtrations of Lie algebras and groups -- A necessary condition for compact presentability -- Implications of the necessary condition -- The second homology -- S-arithmetic groups -- S-arithmetic solvable groups.
The problem of determining which S-arithmetic groups have a finite presentation is solved for arbitrary linear algebraic groups over finite extension fields of #3. For certain solvable topological groups this problem may be reduced to an analogous problem, that of compact presentability. Most of this monograph deals with this question. The necessary background material and the general framework in which the problem arises are given partly in a detailed account, partly in survey form. In the last two chapters the application to S-arithmetic groups is given: here the reader is assumed to have some background in algebraic and arithmetic group. The book will be of interest to readers working on infinite groups, topological groups, and algebraic and arithmetic groups.
9783540471981
10.1007/BFb0079708 doi
Group theory.
Topological Groups.
Group Theory and Generalizations.
Topological Groups, Lie Groups.
QA174-183
512.2