• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1169-1183
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• 2015

We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.297-308
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• 2000

We survey results, obtained in the past three years, on characterizing bounded (and Kobayashi-hyperbolic) Reinhardt domains by their automorphism groups. Specifically, we consider the following two situations: (i) the group is non-compact, and (ii) the dimension of the group is sufficiently large. In addition, we prove two theorems on characterizing general hyperbolic complex manifolds by the dimensions of their automorphism groups.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.487-501
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• 2003

The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in \mathbb{C}^n under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in \mathbb{C}^n does not exceed n.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1145-1153
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• 2014

Let G be a finite group and X be a union of conjugacy classes of G. Define C(G,X) to be the graph with vertex set X and $x,y{\in}X$ ($x{\neq}y$) joined by an edge whenever they commute. In the case that X = G, this graph is named commuting graph of G, denoted by ${\Delta}(G)$. The aim of this paper is to study the automorphism group of the commuting graph. It is proved that Aut(${\Delta}(G)$) is abelian if and only if ${\mid}G{\mid}{\leq}2$; ${\mid}Aut({\Delta}(G)){\mid}$ is of prime power if and only if ${\mid}G{\mid}{\leq}2$, and ${\mid}Aut({\Delta}(G)){\mid}$ is square-free if and only if ${\mid}G{\mid}{\leq}3$. Some new graphs that are useful in studying the automorphism group of ${\Delta}(G)$ are presented and their main properties are investigated.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1043-1049
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• 2016

In this paper we study questions about automorphism groups of domains in ${\mathbb{C}}^n$, formulating the ideas entirely in terms of metric geometry. We also provide some applications.

• Kyungpook Mathematical Journal
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• v.63 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.545-551
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• 2003

We define subalgebras ${V_q}^{mZ{\times}nZ}\;of\;V_q\;where\;V_q$ are in the paper [4]. We show that the Lie algebra ${V_q}^{mZ{\times}nZ}$ is simple and maximally abelian decomposing. We may define a Lie algebra is maximally abelian decomposing, if it has a maximally abelian decomposition of it. The F-algebra automorphism group of the Laurent extension of the quantum plane is found in the paper [4], so we find the Lie automorphism group of ${V_q}^{mZ{\times}nZ}$ in this paper.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.193-210
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• 1997

In this paper we find the irreducible complex characters of the automorphism group of the general linear group of degree 7 over a field with two elements. It is shown that this group has 114 irreducible complex characters.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.677-688
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• 2017

Let P be a finitely generated projective module over a commutative ring R with identity. If P has finite rank, then it will be shown that the map ${\varphi}:Aut_R(P){\rightarrow}U(R)$ defined by ${\varphi}({\alpha})={\det}({\alpha})$ is locally surjective and $Ker({\varphi})=SL_R(P)$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.479-486
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• 2016

The norm N(G) of a group G is the intersection of the normalizers of all the subgroups of G. In this paper, the structure of finite groups with a cyclic norm quotient is determined. As an application of the result, an interesting characteristic of cyclic groups is given, which asserts that a finite group G is cyclic if and only if Aut(G)/P(G) is cyclic, where P(G) is the power automorphism group of G.