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Published by disserta Verlag 2022-06-01, 2022
ISBN 10: 3959355947ISBN 13: 9783959355940
Seller: Chiron Media, Wallingford, United Kingdom
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Published by Disserta Verlag, 2015
ISBN 10: 3959351844ISBN 13: 9783959351843
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.
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Published by Disserta Verlag, 2015
ISBN 10: 3959351860ISBN 13: 9783959351867
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.
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Published by Disserta Verlag, 2015
ISBN 10: 3959351607ISBN 13: 9783959351607
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.
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Published by disserta verlag, 2015
ISBN 10: 3959351100ISBN 13: 9783959351102
Seller: Ria Christie Collections, Uxbridge, United Kingdom
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Condition: New. PRINT ON DEMAND Book; New; Fast Shipping from the UK. No. book.
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Published by disserta verlag, 2015
ISBN 10: 3959351763ISBN 13: 9783959351768
Seller: Ria Christie Collections, Uxbridge, United Kingdom
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Published by Anchor Academic Publishing Dez 2019, 2019
ISBN 10: 3960672241ISBN 13: 9783960672241
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this book we analyse unit groups of group algebras KG for non-abelian p-groups G and fields K of characteristic p. By calculating the core and the normaliser of U in 1 + rad(KG) - the group of normalized units -- for every subgroup U of G, we generalise results of K.R. Pearson and D.B. Coleman using fixed points of enhanced group actions.Our concept of so-called end-commutable ordering leads to a new method of studying the center of 1 + rad(KG). We proof that a finite group G is nilpotent if and only if every conjugacy class possesses an end-commutable ordering. As a simple consequence we get a result of A.A. Bovdi and Z. Patay, which shows how the exponent of the center of 1 + rad(KG) can be determined by calculations purely within the group G.We describe the groups for which this exponent is extremal and calculate the exponent for various group classes (e.g. regular groups, special groups, Sylow subgroups of linear and symmetric groups) and group constructions (e.g. wreath products, central products, special group extensions, isoclinic groups).Another application of our concept of end-commutable ordering is a description of the invariants of the center of 1 + rad(KG) for a finite field K. They are determined purely by the group G and the field K and can be visualized by a special graph - the class-graph.As a consequence of our results we prove that the center, the derived subgroups and the p-th-power subgroup of 1 + rad(KG) are not cyclic. Furthermore, we obtain some properties of unit groups of group algebras for extra-special 2-groups and fields of characteristic 2.Finally, we investigate the behaviour of the center and other characteristics (e.g. the exponent, the class of nilpotency, the Baer length, the degree of commutativity) for the chain of iterated unit groups of modular group algebras. For this, we use Lie and radical algebra methods. 204 pp. Englisch.
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Published by Anchor Academic Publishing Dez 2016, 2016
ISBN 10: 3960671032ISBN 13: 9783960671039
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -During the author's doctorate time at the Christian-Albrechts-Universitat to Kiel Salvatore Siciliano gave a stimulating talk in the upper seminar algebra theory about Cartan subalgebras in Lie algebra associates to associative algebra. This talk was the incentive for the author to analyze maximal nilpotent substructures of the Lie algebra associated to associative algebras. In the present work Siciliano's theory about Cartan subalgebras is worked off and expanded to different special associative algebra classes. In addition, a second maximal nilpotent substructure is analyzed: the nilradical. Within this analysis the main focus is to describe these substructure with the associative structure of the underlying algebra. This is successfully realized in this work. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory. 244 pp. Englisch.
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Published by Anchor Academic Publishing Nov 2017, 2017
ISBN 10: 3960671962ISBN 13: 9783960671961
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Within series II we extend the theory of maximal nilpotent substructures to solvable associative algebras, especially for their group of units and their associated Lie algebra.We construct all maximal nilpotent Lie subalgebras and characterize them by simple and double centralizer properties. They possess distinctive attractor and repeller characteristics. Their number of isomorphic classes is finite and can be bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are extremal among all maximal nilpotent Lie subalgebras.The maximal nilpotent Lie subalgebras are connected to the maximal nilpotent subgroups. This correspondence is bijective via forming the group of units and creating the linear span. Cartan subalgebras and Carter subgroups as well as the Lie nilradical and the Fitting subgroup are linked by this correspondence. All partners possess the same class of nilpotency based on a theorem of Xiankun Du.By using this correspondence we transfer all results to maximal nilpotent subgroups of the group of units. Carter subgroups and the Fitting subgroup turn out to be extremal among all maximal nilpotent subgroups.All four extremal substructures are proven to be Fischer subgroups, Fischer subalgebras, nilpotent injectors and projectors.Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory. 196 pp. Englisch.
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Published by Anchor Academic Publishing Dez 2018, 2018
ISBN 10: 3960672217ISBN 13: 9783960672210
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Within the context of the Wedderburn-Malcev theorem a radical complement exists and all complements are conjugated. The main topics of this work are to analyze the Determination of a (all) radical complements, the representation of an element as the sum of a nilpotent and fully separable element and the compatibility of the Wedderburn-Malcev theorem with derived structures. Answers are presented in details for commutative and solvable associative algebras. Within the analysis the set of fully-separable elements and the generalized Jordan decomposition are of special interest. We provide examples based on generalized quaternion algebras, group algebras and algebras of traingular matrices over a field. The results (and also the theorem of Wedderburn-Malcev and Taft) are transferred to non-unitary algebras by using the star-composition and the adjunction of an unit. Within the App endix we present proofs for the Wedderburn-Malcev theorem for unitary algebras, for Taft's theorem on G-invariant radical complements for unitary algebras and for a theorem of Bauer concerning solvable unit groups of associative algebras. 260 pp. Englisch.
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