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The Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2), John Guaschi; Daniel Juan-Pineda; Silvia Mill?n L?


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Автор: John Guaschi; Daniel Juan-Pineda; Silvia Mill?n L?
Название:  The Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2)
ISBN: 9783319994888
Издательство: Springer
Классификация:



ISBN-10: 3319994883
Обложка/Формат: Soft cover
Страницы: 80
Вес: 0.16 кг.
Дата издания: 2018
Серия: SpringerBriefs in Mathematics
Язык: English
Издание: 1st ed. 2018
Иллюстрации: 4 illustrations, black and white; x, 80 p. 4 illus.
Размер: 234 x 156 x 5
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the results reveal new K-theoretical phenomena with respect to the previous study of other families of groups. The second part of the manuscript focusses on the case of the 4-string braid group of the 2-sphere, which is shown to be hyperbolic in the sense of Gromov. This permits the computation of the infinite maximal virtually cyclic subgroups of this group and their conjugacy classes, and applying the fact that this group satisfies the Fibred Isomorphism Conjecture of Farrell and Jones, leads to an explicit calculation of its lower K-theory. Researchers and graduate students working in K-theory and surface braid groups will constitute the primary audience of the manuscript, particularly those interested in the Fibred Isomorphism Conjecture, and the computation of Nil groups and the lower algebraic K-groups of group rings. The manuscript will also provide a useful resource to researchers who wish to learn the techniques needed to calculate lower algebraic K-groups, and the bibliography brings together a large number of references in this respect.
Дополнительное описание: Introduction.- Lower algebraic K-theory of the finite subgroups of Bn(S?).- The braid group B4(S?) and the conjugacy classes of its maximal virtually cyclic subgroups.- Lower algebraic K-theory groups of the group ring Z[B4(S?)].- Appendix A: The fibred i


On Non-Generic Finite Subgroups of Exceptional Algebraic Groups

Автор: Alastair J. Litterick
Название: On Non-Generic Finite Subgroups of Exceptional Algebraic Groups
ISBN: 1470428377 ISBN-13(EAN): 9781470428372
Издательство: Mare Nostrum (Eurospan)
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Цена: 77610.00 T
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Описание: The study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.

Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces

Автор: F. Dahmani, V. Guirardel, D. Osin
Название: Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces
ISBN: 1470421941 ISBN-13(EAN): 9781470421946
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
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Описание: Introduces and studies the notions of hyperbolically embedded and very rotating families of subgroups. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes.

Discrete Subgroups of Lie Groups

Автор: Madabusi S. Raghunathan
Название: Discrete Subgroups of Lie Groups
ISBN: 3642864287 ISBN-13(EAN): 9783642864285
Издательство: Springer
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Цена: 111790.00 T
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Описание: Our interest, by and large, is in a special class of discrete subgroups of Lie groups, viz., lattices (by a lattice in a locally compact group G, we mean a discrete subgroup H such that the homogeneous space GJ H carries a finite G-invariant measure). It is assumed that the reader has considerable familiarity with Lie groups and algebraic groups.

Abstract Root Subgroups and Simple Groups of Lie-Type

Автор: Franz G. Timmesfeld
Название: Abstract Root Subgroups and Simple Groups of Lie-Type
ISBN: 3034875967 ISBN-13(EAN): 9783034875967
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups.

Discrete Subgroups of Semisimple Lie Groups

Автор: Gregori A. Margulis
Название: Discrete Subgroups of Semisimple Lie Groups
ISBN: 3642057217 ISBN-13(EAN): 9783642057212
Издательство: Springer
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Цена: 167660.00 T
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Описание: This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. The author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature.

Complementation of Normal Subgroups: In Finite Groups

Автор: Joseph Kirtland
Название: Complementation of Normal Subgroups: In Finite Groups
ISBN: 311047879X ISBN-13(EAN): 9783110478792
Издательство: Walter de Gruyter
Цена: 107790.00 T
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Описание:

Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations.

Contents
Prerequisites
The Schur-Zassenhaus theorem: A bit of history and motivation
Abelian and minimal normal subgroups
Reduction theorems
Subgroups in the chief series, derived series, and lower nilpotent series
Normal subgroups with abelian sylow subgroups
The formation generation
Groups with specific classes of subgroups complemented


The Local Structure for Finite Groups With a Large $p$-Subgroup

Автор: U. Meierfrankenfeld, B. Stellmacher, G. Stroth
Название: The Local Structure for Finite Groups With a Large $p$-Subgroup
ISBN: 1470418770 ISBN-13(EAN): 9781470418779
Издательство: Mare Nostrum (Eurospan)
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Цена: 108110.00 T
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Описание: Let $p$ be a prime, $G$ a finite $\mathcal{K}_p$-group $S$ a Sylow $p$-subgroup of $G$ and $Q$ a large subgroup of $G$ in $S$ (i.e., $C_G(Q) \leq Q$ and $N_G(U) \leq N_G(Q)$ for $1 \ne U \leq C_G(Q)$). Let $L$ be any subgroup of $G$ with $S\leq L$, $O_p(L)\neq 1$ and $Q\ntrianglelefteq L$. In this paper the authors determine the action of $L$ on the largest elementary abelian normal $p$-reduced $p$-subgroup $Y_L$ of $L$.

Cyclic Renormalization and Automorphism Groups of Rooted Trees

Автор: Hyman Bass; Maria V. Otero-Espinar; Daniel Rockmor
Название: Cyclic Renormalization and Automorphism Groups of Rooted Trees
ISBN: 3540605959 ISBN-13(EAN): 9783540605959
Издательство: Springer
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Цена: 32600.00 T
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Описание: The theme of this monograph is an interplay between dynamical systems and group theory. The normal subgroup structure of the automorhpism groups of such "spherically homogenous" rooted trees is investigated in detail.

Quilts: Central Extensions, Braid Actions, and Finite Groups

Автор: Tim Hsu
Название: Quilts: Central Extensions, Braid Actions, and Finite Groups
ISBN: 3540673970 ISBN-13(EAN): 9783540673972
Издательство: Springer
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Цена: 27910.00 T
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Braid Groups

Автор: Christian Kassel; O. Dodane; Vladimir Turaev
Название: Braid Groups
ISBN: 1441922202 ISBN-13(EAN): 9781441922205
Издательство: Springer
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Цена: 55890.00 T
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Описание: The authors introduce the basic theory of braid groups, highlighting several definitions showing their equivalence. This is followed by a treatment of the relationship between braids, knots and links. Important results then look at linearity and orderability.


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