• 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.

• 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.

• East Asian mathematical journal
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• v.31 no.3
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• pp.363-370
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• 2015

The automorphism group of domains is main stream of classification problem coming from E. Cartan's work. In this paper, I introduce classical technique of computations of automorphism group of domains and recent development of automorphism group. Moreover, I suggest new research problems in computations of automorphism group.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1427-1437
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• 2023

It is known that the automorphism group of a K3 surface with Picard number two is either an infinite cyclic group or an infinite dihedral group when it is infinite. In this paper, we study the generators of such automorphism groups. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators.

• 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.

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.681-693
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• 2003

In this paper, we first prove that there are no automorphism orbits accumulating at a boundary point of the largest isolated finite type. We also present a generalization of the results of Isaev and Krantz on the structure of the orbit accumulation points.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.575-584
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• 1996

We investigate how the code automorphism groups can be used to study such combinatorial objects as codes, finite projective planes and Hadamard matrices. For this purpose, we write down a computer program for computing code automorphisms in PASCAL language. Then we study the combinatorial properties using those code automorphism group algorithms and the relationship between combinatorial objects and codes.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.927-938
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• 2016

In this note, we study a monodromy map of a fibered 2-bridge knot. We show the monodromy map of a fibered 2-bridge knot as an element in the automorphism group of a free group.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.171-177
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• 1993

In this paper, we show that Greene-Krantz's conjecture is true for certain class of domains. In fact, we give a complete classification of automorphism groups of domains of the form (Fig.) where the function .phi. is a real valued $C^{\infty}$ function in a neighborhood of [0,1] which satisfies the following conditions; (1) .phi.(0)=.phi.'(0)=0 and .phi.(1)=1, (2) .phi.(t) is increasing and convex for t>0.vex for t>0.