Fundamentals of Group Theory (Record no. 59878)

MARC details
000 -LEADER
fixed length control field 03837nam a22004455i 4500
001 - CONTROL NUMBER
control field 978-0-8176-8301-6
003 - CONTROL NUMBER IDENTIFIER
control field DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20251006084441.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 111024s2012 xxu| s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780817683016
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 99780817683016
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-0-8176-8301-6
Source of number or code doi
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.2
Edition information 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Roman, Steven.
Relator term author.
245 10 - TITLE STATEMENT
Title Fundamentals of Group Theory
Medium [electronic resource] :
Remainder of title An Advanced Approach /
Statement of responsibility, etc. by Steven Roman.
250 ## - EDITION STATEMENT
Edition statement 1.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Boston :
Name of producer, publisher, distributor, manufacturer Birkhäuser Boston,
Date of production, publication, distribution, manufacture, or copyright notice 2012.
300 ## - PHYSICAL DESCRIPTION
Extent XII, 380p. 21 illus.
Other physical details online resource.
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
347 ## - DIGITAL FILE CHARACTERISTICS
File type text file
Encoding format PDF
Source rda
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 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 ## - SUMMARY, ETC.
Summary, etc. 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 groups 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 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element MATHEMATICS.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element ALGEBRA.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element GROUP THEORY.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element MATHEMATICS.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element GROUP THEORY AND GENERALIZATIONS.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element ALGEBRA.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element ORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Printed edition:
International Standard Book Number 9780817683009
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="http://dx.doi.org/10.1007/978-0-8176-8301-6">http://dx.doi.org/10.1007/978-0-8176-8301-6</a>
Public note Ver el texto completo en las instalaciones del CICY
912 ## -
-- ZDB-2-SMA
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Dewey Decimal Classification
Koha item type Libros electrónicos
Holdings
Lost status Source of classification or shelving scheme Damaged status Not for loan Collection Home library Current library Shelving location Date acquired Total checkouts Full call number Date last seen Price effective from Koha item type
  Dewey Decimal Classification     Libro electrónico CICY CICY Libro electrónico 06.10.2025   512.2 06.10.2025 06.10.2025 Libros electrónicos