• East Asian mathematical journal
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• v.15 no.1
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• pp.45-53
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• 1999

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.49-59
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• 2001

In this paper, we introduce an extended notion of regular homomorphism of minimal sets by considering a certain subgroup of the group of automorphisms of a universal minimal transfomation group.

• 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.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1199-1211
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• 2013

We introduce a new class of graphs, called quasi $m$-Cayley graphs, having good symmetry properties, in the sense that they admit a group of automorphisms G that fixes a vertex of the graph and acts semiregularly on the other vertices. We determine when these graphs are strongly regular, and this leads us to define a new algebro-combinatorial structure, called quasi-partial difference family, or QPDF for short. We give several infinite families and sporadic examples of QPDFs. We also study several properties of QPDFs and determine, under several conditions, the form of the parameters of QPDFs when the group G is cyclic.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.45-52
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• 2006

Every non-associative algebra L corresponds to its symmetric semi-Lie algebra $L_{[,]}$ with respect to its commutator. It is an interesting problem whether the equality $Aut{non}(L)=Aut_{semi-Lie}(L)$ holds or not [2], [13]. We find the non-associative algebra automorphism groups $Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ and $Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ where every automorphism of the automorphism groups is the composition of elementary maps [3], [4], [7], [8], [9], [10], [11]. The results of the paper show that the F-algebra automorphism groups of a polynomial ring and its Laurent extension make easy to find the automorphism groups of the algebras in the paper.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.653-666
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• 2020

In this paper, when G is a connected and simply connected nilpotent Lie group of dimension less than or equal to four, we study the uniform lattices Γ of G up to isomorphism and then we study the structure of the automorphism group Aut(Γ) of Γ from the viewpoint of splitting as a natural extension.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.123-129
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• 1998

In this paper, we study some dynamical properties of a weakly almost periodic flow. In particular we get, in a weakly almost periodic flow (X,T), the groups I and A(I) of all automorphisms of I are isomorphic, where E(X) is the enveloping semigroup of (X,T) and I is the minimal right ideal in E(X).

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.643-652
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• 2022

In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1097-1105
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• 2015

The concept of tensor analogues of right 2-Engel elements in groups were defined and studied by Biddle and Kappe [1] and Moravec [9]. Using the automorphisms of a given group G, we introduce the notion of tensor analogue of 2-auto Engel elements in G and investigate their properties. Also the concept of $2_{\otimes}$-auto Engel groups is introduced and we prove that if G is a $2_{\otimes}$-auto Engel group, then $G{\otimes}$ Aut(G) is abelian. Finally, we construct a non-abelian 2-auto-Engel group G so that its non-abelian tensor product by Aut(G) is abelian.