000 02630nam a22004695i 4500
001 978-88-470-2421-2
003 DE-He213
005 20140220083335.0
007 cr nn 008mamaa
008 120405s2012 it | s |||| 0|eng d
020 _a9788847024212
_9978-88-470-2421-2
024 7 _a10.1007/978-88-470-2421-2
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
082 0 4 _a512
_223
100 1 _aMachì, Antonio.
_eauthor.
245 1 0 _aGroups
_h[electronic resource] :
_bAn Introduction to Ideas and Methods of the Theory of Groups /
_cby Antonio Machì.
264 1 _aMilano :
_bSpringer Milan :
_bImprint: Springer,
_c2012.
300 _aXIII, 371 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUNITEXT,
_x2038-5714
505 0 _aNormal Subgroups, Conjugation and Isomorphism Theorems -- Group Actions and Permutation Groups -- Generators and Relations -- Nilpotent Groups and Solvable Groups -- Representations -- Extensions and Cohomology -- Solution to the exercises.
520 _aGroups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aGroup theory.
650 1 4 _aMathematics.
650 2 4 _aAlgebra.
650 2 4 _aGroup Theory and Generalizations.
650 2 4 _aCommutative Rings and Algebras.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9788847024205
830 0 _aUNITEXT,
_x2038-5714
856 4 0 _uhttp://dx.doi.org/10.1007/978-88-470-2421-2
912 _aZDB-2-SMA
999 _c104134
_d104134