LEADER 03773nam 2200721Ia 450 001 9910811251603321 005 20200520144314.0 010 $a1-107-18521-1 010 $a1-281-15366-4 010 $a9786611153663 010 $a1-139-13345-4 010 $a0-511-35537-8 010 $a0-511-35487-8 010 $a0-511-35429-0 010 $a0-511-54275-5 010 $a0-511-35589-0 035 $a(CKB)1000000000481100 035 $a(EBL)321355 035 $a(OCoLC)190643124 035 $a(SSID)ssj0000148159 035 $a(PQKBManifestationID)11150859 035 $a(PQKBTitleCode)TC0000148159 035 $a(PQKBWorkID)10225018 035 $a(PQKB)11639858 035 $a(UkCbUP)CR9780511542756 035 $a(Au-PeEL)EBL321355 035 $a(CaPaEBR)ebr10209487 035 $a(CaONFJC)MIL115366 035 $a(MiAaPQ)EBC321355 035 $a(PPN)261308963 035 $a(EXLCZ)991000000000481100 100 $a20071109d2007 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEnumeration of finite groups /$fSimon R. Blackburn, Peter M. Neumann, Geetha Venkataraman 205 $a1st ed. 210 $aCambridge $cCambridge University Press$d2007 215 $a1 online resource (xii, 281 pages) $cdigital, PDF file(s) 225 1 $aCambridge tracts in mathematics ;$v173 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-88217-6 320 $aIncludes bibliographical references and index. 327 $aSome basic observations -- Preliminaries -- Enumerating p-groups: a lower bound -- Enumerating p-groups: upper bounds -- Some more preliminaries -- Group extensions and cohomology -- Some representation theory -- Primitive soluble linear groups -- The orders of groups -- Conjugacy classes of maximal soluble subgroups of symmetric groups -- Enumeration of finite groups with abelian Sylow subgroups -- Maximal soluble linear groups -- Conjugacy classes of maximal soluble subgroups of the general linear groups -- Pyber's theorem: the soluble case -- Pyber's theorem: the general case -- Enumeration within varieties of abelian groups -- Enumeration within small varieties of A-groups -- Enumeration within small varieties of p-groups. 330 $aHow many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of how a group may be presented by generators and relations, a very little representation theory from the perspective of module theory, and a very little cohomology theory - but most of the basics are expounded here and the book is more or less self-contained. Although it is principally devoted to a connected exposition of an agreeable theory, the book does also contain some material that has not hitherto been published. It is designed to be used as a graduate text but also as a handbook for established research workers in group theory. 410 0$aCambridge tracts in mathematics ;$v173. 606 $aFinite groups 606 $aMathematics 615 0$aFinite groups. 615 0$aMathematics. 676 $a512.23 700 $aBlackburn$b Simon R$01605453 701 $aNeumann$b P. M$01756724 701 $aVenkataraman$b Geetha$01756725 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811251603321 996 $aEnumeration of finite groups$94194186 997 $aUNINA