• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1015-1021
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• 2011

A point of a Riemann surface X is said to be its fixed point if it is a fixed point of one of its nontrivial holomorphic automorphisms. We start this note by proving that the set Fix(X) of fixed points of Riemann surface X of genus g${\geq}$2 has at most 82(g-1) elements and this bound is attained just for X having a Hurwitz group of automorphisms, i.e., a group of order 84(g-1). The set of such points is invariant under the group of holomorphic automorphisms of X and we study the corresponding symmetric representation. We show that its algebraic type is an essential invariant of the topological type of the holomorphic action and we study its kernel, to find in particular some sufficient condition for its faithfulness.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.73-79
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• 2003

A subgroup S(X, ${\gamma}$) of the group of automorphisms of a universal minimal transformation group is introduced and a necessary and sufficient condition for two subgroups to be identical is obtained.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.27-60
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• 1996

We compute low order terms of automorphisms of a quadric CR manifold defined by $v^a$ =< $A^az$, z > where there is a real vector ${\kappa}{\in}R^m$ such that $det({\kappa}{\cdot}A){\neq}0$.

• Journal of applied mathematics & informatics
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• v.9 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.247-251
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• 1988

This note gives a combinatorial treatment to the problem finding a generating set among conjugating automorphisms of a free group and to the method deciding when a conjugating endomorphism of a free group is an automorphism. Our group of pseudo-conjugating automorphisms can be thought of as a generalization of the artin's braid group.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.759-769
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• 2006

Let L : $C\;\rightarrow\;C$ be a hyperbolic automorphism. Then the hyperbolic toral automorphism $L_A\;T^2\;\rightarrow\;T^2$, induced by L, is a chaotic map ([2] pg.192). We characterize hyperbolic toral automorphisms by proving the converse of the above statement.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.335-353
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• 2024

The objective of this paper is to study some central identities involving generalized derivations and anti-automorphisms in prime rings. Using the tools of the theory of functional identities, several known results have been generalized as well as improved.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.301-309
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• 2011

Let R = $Mat_2(F)$ be the ring of all 2 by 2 matrices over a finite field F, X the set of all nonzero, nonunits of R and G the group of all units of R. After investigating some properties of orbits under the left (and right) regular action on X by G, we show that the graph automorphisms group of $\Gamma(R)$ (the zero-divisor graph of R) is isomorphic to the symmetric group $S_{|F|+1}$ of degree |F|+1.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.847-851
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• 2011

In this paper we provide examples of pairs of conformally non-equivalent, but topologically equivalent, p-groups $H_1$, $H_2$ < Aut(S), where S is a closed Riemann surface of genus g ${\geq}$ 2, so that $S/H_j$ has genus zero and all its cone points are of order equal to p.