• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.709-718
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• 2023

The inner automorphism groups of quandles are related to the classification problem of quandles. The inner automorphism group of a quandle is generated by inner automorphisms which are presented by columns in the operation table of the quandle. In this paper, we describe inner automorphisms of an abelian extension of a quandle by expressing columns of the operation table of the extended quandle as columns of the operation table of the original quandle. Such a description will be helpful in studying inner automorphism groups of abelian extensions of quandles.

• 대한수학회보
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• 제49권5호
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• pp.949-959
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• 2012

In general, a class-preserving automorphism of generalized free products of nilpotent groups, amalgamating a cyclic normal subgroup of order 8, need not be an inner automorphism. We prove that every class-preserving automorphism of generalized free products of nitely generated nilpotent groups, amalgamating a cyclic normal subgroup of order less than 8, is inner.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.859-867
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• 2002

In this paper, we get a necessary and sufficient condition for an inner automorphism between compact connected semisimple Lie groups to be an atone transformation, and obtain atone transformations of (SU(n),g) with some left invariant metric g.

• Kyungpook Mathematical Journal
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• 제57권4호
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• pp.711-719
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• 2017

Let Inn(Q) denote the inner automorphism group on a quandle Q. For a subset M of Q, let c(M) denote the orbit of M under the Inn(Q)-action on Q. Then c satisfies the axioms of the closure operator. In this paper, we study the topological space Q corresponding to the topology obtained from the closure operator c.

• 대한수학회보
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• 제53권4호
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• pp.1033-1041
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• 2016

We show that, for any non-zero integers ${\lambda}$, ${\mu}$, ${\nu}$, ${\xi}$, class-preserving automorphisms of the group $$G({\lambda},{\mu},{\nu},{\xi})={\langle}a,b,t:b^{-1}a^{\lambda}b=a^{\mu},t^{-1}a^{\nu}t=b^{\xi}{\rangle}$$ are all inner. Hence, by using Grossman's result, the outer automorphism group of $G({\lambda},{\pm}{\lambda},{\nu},{\xi})$ is residually finite.

• 대한수학회보
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• 제58권4호
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• pp.973-981
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• 2021

Let R be a commutative ring with identity 1, n ≥ 3, and let 𝒯_n(R) be the linear Lie algebra of all upper triangular n × n matrices over R. A linear map 𝜑 on 𝒯_n(R) is called to be strong commutativity preserving if [𝜑(x), 𝜑(y)] = [x, y] for any x, y ∈ 𝒯_n(R). We show that an invertible linear map 𝜑 preserves strong commutativity on 𝒯_n(R) if and only if it is a composition of an idempotent scalar multiplication, an extremal inner automorphism and a linear map induced by a linear function on 𝒯_n(R).

• 호남수학학술지
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• 제28권2호
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• pp.197-204
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• 2006

For the evaluation algebra $F[e^{{\pm}{\chi}}]_M$, if M={$\partial$}, the automorphism group $Aut_{non}$($F[e^{{\pm}{\chi}}]_M$) and $Der_{non}$($F[e^{{\pm}{\chi}}]_M$) of the evaluation algebra $F[e^{{\pm}{\chi}}]_M$ are found in the paper [12]. For M={${\partial}^n$}, we find $Aut_{non}$($F[e^{{\pm}{\chi}}]_M$) and $Der_{non}$($F[e^{{\pm}{\chi}}]_M$) of the evaluation algebra $F[e^{{\pm}{\chi}}]_M$ in this paper. We show that a derivation of some non-associative algebra is not inner.