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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Automorphisms of Finite Groups (Hardcover, 1st ed. 2018)
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Automorphisms of Finite Groups (Hardcover, 1st ed. 2018)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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The 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.
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