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- W4312917085 abstract "Abstract The normalizer problem of integral group rings has been studied extensively in recent years due to its connection with the longstanding isomorphism problem of integral group rings. Class-preserving Coleman automorphisms of finite groups occur naturally in the study of the normalizer problem. Let <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>G</m:mi> </m:math> G be a finite group with a nilpotent subgroup <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>N</m:mi> </m:math> N . Suppose that <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>G</m:mi> <m:mspace width=-0.0em /> <m:mtext>/</m:mtext> <m:mspace width=-0.0em /> <m:mi>N</m:mi> </m:math> Ghspace{-0.0em}text{/}hspace{-0.0em}N acts faithfully on the center of each Sylow subgroup of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>N</m:mi> </m:math> N . Then it is proved that every class-preserving Coleman automorphism of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>G</m:mi> </m:math> G is an inner automorphism. In addition, if <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>G</m:mi> </m:math> G is the product of a cyclic normal subgroup and an abelian subgroup, then it is also proved that every class-preserving Coleman automorphism of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>G</m:mi> </m:math> G is an inner automorphism. Other similar results are also obtained in this article. As direct consequence, the normalizer problem has a positive answer for such groups." @default.
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- W4312917085 date "2022-01-01" @default.
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- W4312917085 title "Class-preserving Coleman automorphisms of some classes of finite groups" @default.
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- W4312917085 doi "https://doi.org/10.1515/math-2022-0521" @default.
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