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Automorphisms of Coxeter Groups of Rank 3 with Infinite Bonds

โœ Scribed by W.N. Franzsen

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
138 KB
Volume
248
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

If W is a rank 3 Coxeter group, whose Coxeter diagram contains at least one infinite bond, then the automorphism group of W is larger than the group generated by the inner automorphisms and the automorphisms induced from automorphisms of the Coxeter diagram. In each case the automorphism group of W is described.

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Let k be an imaginary quadratic number field with C k, 2 , the 2-Sylow subgroup of its ideal class group, isomorphic to Zร‚2Z\_Zร‚2Z\_Zร‚2Z. By the use of various versions of the Kuroda class number formula, we improve significantly upon our previous lower bound for |C k 1 , 2 | , the 2-class number of