Fundamentals of Group Theory An Advanced Approach /

Fundamentals of Group Theory provides an advanced look at the basic theory of groups. Standard topics in the field are covered alongside a great deal of unique content. There is an emphasis on universality when discussing the isomorphism theorems, quotient groups and free groups as well as a focus o...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Roman, Steven (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
Edición:1st ed. 2012.
Temas:
Group theory.
Algebra.
Group Theory and Generalizations.
Order, Lattices, Ordered Algebraic Structures.
Acceso en línea:Texto Completo

MARC

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100 1 |a Roman, Steven.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Fundamentals of Group Theory  |h [electronic resource] :  |b An Advanced Approach /  |c by Steven Roman. 
250 |a 1st ed. 2012. 
264 1 |a Boston, MA :  |b Birkhäuser Boston :  |b Imprint: Birkhäuser,  |c 2012. 
300 |a XII, 380 p. 21 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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505 0 |a Preliminaries -- Groups and Subgroups -- Cosets, Index and Normal Subgroups -- Homomorphisms -- Chain Conditions and Subnormality -- Direct and Semidirect Products -- Permutation Groups -- Group Actions -- The Structure of -Groups -- Sylow Theory -- The Classification Problem for Groups -- Finiteness Conditions -- Free Groups and Presentations -- Abelian Groups -- References. 
520 |a Fundamentals of Group Theory provides an advanced look at the basic theory of groups. Standard topics in the field are covered alongside a great deal of unique content. There is an emphasis on universality when discussing the isomorphism theorems, quotient groups and free groups as well as a focus on the role of applying certain operations, such as intersection, lifting and quotient to a "group extension". Certain concepts, such as subnormality, group actions and chain conditions are introduced perhaps a bit earlier than in other texts at this level, in the hopes that the reader would acclimate to these concepts earlier.  Some additional features of the work include:  An historical look at how Galois viewed groups. The problem of whether the commutator subgroup of a group is the same as the set of commutators of the group, including an example of when this is not the case. The subnormal join property, that is, the property that the join of two subnormal subgroups is subnormal. Cancellation in direct sums. A complete proof of the theorem of Baer characterizing nonabelian groups with the property that all of their subgroups are normal. A somewhat more in depth discussion of the structure of p-groups, including the nature of conjugates in a p-group, a proof that a p-group with a unique subgroup of any order must be either cyclic (for p>2) or else cyclic or generalized quaternion (for p=2) and the nature of gro ups of order p^n that have elements of order p^(n-1). A discussion of the Sylow subgroups of the symmetric group in terms of wreath products. An introduction to the techniques used to characterize finite simple groups. Birkhoff's theorem on equational classes and relative freeness. This book is suitable for a graduate course in group theory, part of a graduate course in abstract algebra or for independent study. It can also be read by advanced undergraduates. The book assumes no specific background in group theory, but does assume some level of mathematical sophistication on the part of the reader. 
650 0 |a Group theory. 
650 0 |a Algebra. 
650 1 4 |a Group Theory and Generalizations. 
650 2 4 |a Algebra. 
650 2 4 |a Order, Lattices, Ordered Algebraic Structures. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9780817683009 
776 0 8 |i Printed edition:  |z 9780817683023 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-0-8176-8301-6  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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