• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권3호
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• pp.283-296
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• 2009

Let f(x) = $x^n\;+\;a$ be a binomial polynomial in Z[x] and $f_m(x)$ be the m-th iterate of f(x). In this work we study a necessary condition to be the Galois group of $f_m(x)$ is isomorphic to a wreath product group $[C_n]^m$ where $C_n$ is a cyclic group of order n.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.915-931
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• 2009

The non-rigid molecule group theory in which the dynamical symmetry operations are defined as physical operations is applied to deduce the character table of the full non-rigid molecule group (f-NRG) of 2,3,5,6-Tetramethylpyrazine The f-NRG of this molecule is seen to be isomorphic to the group $\mathbb{Z}_3{\wr}(\mathbb{Z}_2{\times}\mathbb{Z}_2)$, where $\mathbb{Z}_n$ is the cyclic group of order n, of order 324 which has 45 conjugacy classes. We determine the some properties and relations between characters of the group. Also, we examine the symmetry group of this molecule and show that its symmetry group is $\mathbb{Z}_2{\times}\mathbb{Z}_2$.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.669-682
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• 2016

In this paper, we study the cellular structure of the G-edge colored partition algebras, when G is a finite group. Further, we classified all the irreducible representations of these algebras using their cellular structure whenever G is a finite cyclic group. Also we prove that the ${\mathbb{Z}}/r{\mathbb{Z}}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.

• 충청수학회지
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• 제22권3호
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• pp.497-506
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• 2009

This work studies about the composition polynomial f(g(x)) that preserves certain properties of f(x) and g(x). We shall investigate necessary and sufficient conditions of f(x) and g(x) to be f(g(x)) is separable, solvable by radical or split completely. And we find relationship of Galois groups of f(g(x)), f(x) and of g(x).

• 대한수학회보
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• 제30권1호
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• pp.25-27
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• 1993

In our paper [4] we showed that over bar $A_{n-1}$ is a split extension of (n-1) copies of Z by the symmetric group S$_{n}$ of degree n. We show in this paper how over bar $A_{n-1}$ appears naturally as a subgroup of the natural wreath product W=ZS$_{n}$.TEX> n/.