• Korean Journal of Mathematics
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• 제22권3호
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• pp.583-590
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• 2014

In this paper we give some relationships between quasi-Ellis groups and some subgroups of the automorphism group. In particular, we investigate several characterizations on some subgroups of the automorphism group.

• Korean Journal of Mathematics
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• 제21권2호
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• pp.181-187
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• 2013

In this paper we give some results on homomorphisms of pointed minimal sets. In particular, we investigate some characterizations on quasi-Ellis groups.

• 호남수학학술지
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• 제38권1호
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• pp.1-8
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• 2016

In this paper, we get a complete condition for a group homomorphism of a compact Lie group with an arbitrarily given left invariant Riemannian metric into another Lie group with a left invariant metric to be a harmonic map, and then obtain a necessary and sufficient condition for a group homomorphism of (SU(2), g) with a left invariant metric g into the Heisenberg group (H, $h_0$) to be a harmonic map.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.211-217
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• 2011

In this paper we study some properties on regular homomorphisms. In particular, we investigate the equivalent conditions for the homomorphism of minimal sets to be regular.

• Korean Journal of Mathematics
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• 제19권3호
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• pp.273-278
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• 2011

In this paper we give some results on homomorphisms of pointed minimal sets. In particular, we investigate some characterizations on Ellis groups.

• 충청수학회지
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• 제14권1호
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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.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.373-385
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• 2018

In this paper we introduce the notion of a fuzzy kernel of a fuzzy homomorphism on groups and we show that it is a fuzzy normal subgroup of the domain group. Conversely, we also prove that any fuzzy normal subgroup is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fuzzy version of the fundamental theorem of homomorphism and those isomorphism theorems.

• 충청수학회지
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• 제11권1호
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• pp.59-71
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• 1998

In this paper we define a regular relation with respect to a homomorphism in transformation groups and we find the equivalent conditions for the relation to be an equivalence relation.

• 충청수학회지
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• 제21권4호
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• pp.555-562
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• 2008

In this paper, it will be given a necessary and sufficient condition for a function to be an r-homomorphism in connection with the subgroups of the automorphism group of a universal minimal set.

• 대한수학회보
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• 제54권6호
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• pp.2165-2182
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• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.