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On quaternion-free 2-groups

โœ Scribed by Bettina Wilkens

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
183 KB
Volume
258
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

Two theorems are proved, the first of them showing that a modular quaternion-free finite 2-group has a characteristic abelian subgroup with metacyclic factor, the second classifying nonmodular finite quaternion-free 2-groups.

๐Ÿ“œ SIMILAR VOLUMES

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Matrices whose entries belong to certain rings of algebraic integers are known to be associated with discrete groups of transformations of inversive n-space or hyperbolic n 1-space r n1 . In particular, groups operating in the hyperbolic plane or hyperbolic 3-space may be represented by 2 ร‚ 2 matric

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For each of the dihedral, semidihedral, and quaternion 2-groups, we represent the obstructions to certain Brauer problems as tensor products of quaternion algebras. Then we reduce various embedding problems with cyclic 2-kernels into two Brauer problems, thus finding the obstructions in some specifi