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On unit groups of modular group algebras. The concept of end-commutable ordering - with 241 exercises - Tapa blanda
- EditorialAnchor Academic Publishing
- Año de publicación2019
- ISBN 10 3960672241
- ISBN 13 9783960672241
- EncuadernaciónTapa blanda
- Número de páginas204
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On unit groups of modular group algebras
Publicado por
Anchor Academic Publishing Dez 2019
(2019)
ISBN 10: 3960672241
ISBN 13: 9783960672241
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Descripción Taschenbuch. Condición: 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. Nº de ref. del artículo: 9783960672241
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On unit groups of modular group algebras : The concept of end-commutable ordering - with 241 exercises
Publicado por
Anchor Academic Publishing
(2019)
ISBN 10: 3960672241
ISBN 13: 9783960672241
Nuevo
Taschenbuch
Cantidad disponible: 1
Librería:
Valoración
Descripción Taschenbuch. Condición: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9783960672241
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On unit groups of modular group algebras. The concept of end-commutable ordering - with 241 exercises
Publicado por
Anchor Academic Publishing
(2019)
ISBN 10: 3960672241
ISBN 13: 9783960672241
Nuevo
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Descripción Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 . Nº de ref. del artículo: 385837040
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On unit groups of modular group algebras The concept of endcommutable ordering with 241 exercises
Publicado por
Anchor Academic Publishing
(2019)
ISBN 10: 3960672241
ISBN 13: 9783960672241
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Descripción PAP. Condición: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. del artículo: L0-9783960672241
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On unit groups of modular group algebras: The concept of end-commutable ordering - with 241 exercises
Publicado por
Anchor Academic Publishing
(2019)
ISBN 10: 3960672241
ISBN 13: 9783960672241
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Descripción Condición: New. Nº de ref. del artículo: ABLING22Oct2817100641527
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On unit groups of modular group algebras:The concept of end-commutable ordering - with 241 exercises
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Anchor Academic Publishing
(2019)
ISBN 10: 3960672241
ISBN 13: 9783960672241
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Descripción Condición: New. PRINT ON DEMAND Book; New; Fast Shipping from the UK. No. book. Nº de ref. del artículo: ria9783960672241_lsuk
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On unit groups of modular group algebras The concept of endcommutable ordering with 241 exercises
Publicado por
Anchor Academic Publishing
(2019)
ISBN 10: 3960672241
ISBN 13: 9783960672241
Nuevo
PAP
Cantidad disponible: > 20
Librería:
Valoración
Descripción PAP. Condición: New. New Book. Delivered from our UK warehouse in 4 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. del artículo: L0-9783960672241
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