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Fundamentals of Group Theory (Record no. 22716)

000 -LEADER
fixed length control field 03756nam a22004335i 4500
003 - CONTROL NUMBER IDENTIFIER
control field OSt
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20140310151443.0
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
978-0-8176-8301-6
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA174-183
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.2
Edition number 23
264 #1 -
-- Boston :
-- Birkhäuser Boston,
-- 2012.
912 ## -
-- ZDB-2-SMA
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Roman, Steven.
Relator term author.
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE
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.
300 ## - PHYSICAL DESCRIPTION
Extent XII, 380p. 21 illus.
Other physical details online resource.
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 as entry element Mathematics.
Topical term or geographic name as entry element Algebra.
Topical term or geographic name as entry element Group theory.
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element Group Theory and Generalizations.
Topical term or geographic name as entry element Algebra.
Topical term or geographic name as 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
Display text Printed edition:
International Standard Book Number 9780817683009
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://dx.doi.org/10.1007/978-0-8176-8301-6
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type E-Book
Copies
Price effective from Permanent location Date last seen Not for loan Date acquired Source of classification or shelving scheme Koha item type Damaged status Lost status Withdrawn status Current location Full call number
2014-04-09AUM Main Library2014-04-09 2014-04-09 E-Book   AUM Main Library512.2
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