000 03845nam a22004575i 4500
001 978-0-8176-8301-6
003 DE-He213
005 20140220083227.0
007 cr nn 008mamaa
008 111024s2012 xxu| s |||| 0|eng d
020 _a9780817683016
_9978-0-8176-8301-6
024 7 _a10.1007/978-0-8176-8301-6
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
082 0 4 _a512.2
_223
100 1 _aRoman, Steven.
_eauthor.
245 1 0 _aFundamentals of Group Theory
_h[electronic resource] :
_bAn Advanced Approach /
_cby Steven Roman.
250 _a1.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2012.
300 _aXII, 380p. 21 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreliminaries -- 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 _aFundamentals 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 _aMathematics.
650 0 _aAlgebra.
650 0 _aGroup theory.
650 1 4 _aMathematics.
650 2 4 _aGroup Theory and Generalizations.
650 2 4 _aAlgebra.
650 2 4 _aOrder, Lattices, Ordered Algebraic Structures.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817683009
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-8301-6
912 _aZDB-2-SMA
999 _c100237
_d100237