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010   $a981-13-2895-1
024 7 $a10.1007/978-981-13-2895-4
035   $a(CKB)4100000007463608
035   $a(MiAaPQ)EBC5632927
035   $a(DE-He213)978-981-13-2895-4
035   $a(PPN)233796088
035   $a(EXLCZ)994100000007463608
100   $a20190112d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aAutomorphisms of Finite Groups /$fby Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav
205   $a1st ed. 2018.
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2018.
215   $a1 online resource (231 pages)
225 1 $aSpringer Monographs in Mathematics,$x1439-7382
311   $a981-13-2894-3 
327   $aIntroduction -- p-groups -- Fundamental exact sequence of Wells -- Automorphism groups of finite groups -- Groups with Divisibility Property-I -- Groups with Divisibility Property-II -- Groups without Divisibility Property.
330   $aThe book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
410  0$aSpringer Monographs in Mathematics,$x1439-7382
606   $aGroup theory
606   $aTopological groups
606   $aLie groups
606   $aFunctions of complex variables
606   $aNumber theory
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132
606   $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
615  0$aGroup theory.
615  0$aTopological groups.
615  0$aLie groups.
615  0$aFunctions of complex variables.
615  0$aNumber theory.
615 14$aGroup Theory and Generalizations.
615 24$aTopological Groups, Lie Groups.
615 24$aSeveral Complex Variables and Analytic Spaces.
615 24$aNumber Theory.
676   $a512.2
700   $aPassi$b Inder Bir Singh$4aut$4http://id.loc.gov/vocabulary/relators/aut$058117
702   $aSingh$b Mahender$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aYadav$b Manoj Kumar$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910309662603321
996   $aAutomorphisms of Finite Groups$91982515
997   $aUNINA