• 대한수학회보
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• 제51권4호
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• pp.923-931
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• 2014

Let x be an element of a group G and be an automorphism of G. Then for a positive integer n, the autocommutator $[x,_n{\alpha}]$ is defined inductively by $[x,{\alpha}]=x^{-1}x^{\alpha}=x^{-1}{\alpha}(x)$ and $[x,_{n+1}{\alpha}]=[[x,_n{\alpha}],{\alpha}]$. We call the group G to be n-auto-Engel if $[x,_n{\alpha}]=[{\alpha},_nx]=1$ for all $x{\in}G$ and every ${\alpha}{\in}Aut(G)$, where $[{\alpha},x]=[x,{\alpha}]^{-1}$. Also, for any integer $n{\neq}0$, 1, a group G is called an n-auto-Bell group when $[x^n,{\alpha}]=[x,{\alpha}^n]$ for every $x{\in}G$ and each ${\alpha}{\in}Aut(G)$. In this paper, we investigate the properties of such groups and show that if G is an n-auto-Bell group, then the factor group $G/L_3(G)$ has finite exponent dividing 2n(n-1), where $L_3(G)$ is the third term of the upper autocentral series of G. Also, we give some examples and results about n-auto-Bell abelian groups.

• 대한의생명과학회지
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• 제9권2호
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• pp.93-98
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• 2003

To investigate the cyclohexane and xylene mixture treatment on the liver damage, the rats were treated by the mixture of cyclohexane and xylene (CH＋X) and then, liver damage was demonstrated by liver function findings based on liver weight/body weight, serum level of alanine aminotransferase (ALT), xanthine oxidase (XO) and then compared with cyclohexane treated group (CH group) and xylene-treated group (X). The CH＋X group showed merely severer liver damge than CH or X group. On the other hand, CH＋X group showed lower activity of hepatic cytochrome P-450 dependent aniline hydroxylase (CYPdAH) than CH or X group, but no statical differences were demonstrated among three experimental groups. Especially the hepatic GSH content was merely declined than CH or X group and the activity of hepatic GST was higher in CH＋X group than CH or X group. In conclusion, cyclohexane and xylene mixture treated animals showed merely severer liver damage than cyclohexane or xylene treated group and such a fact may be caused by inhibition of cyclohexane or xylene metabolism and oxygen free radical.

• 충청수학회지
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• 제4권1호
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• pp.103-113
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• 1991

Some properties of a path space and the fundamental group ${\sigma}(X,x_0,G)$ of a topological transformation group (X, G, ${\pi}$) are described. It is shown that ${\sigma}(X,x_0,H)$ is a normal subgroup of ${\sigma}(X,x_0,G)$ if H is a normal subgroup of G ; Let (X, G, ${\pi}$) be a transformation group with the open action property. If every identification map $p:{\Sigma}(X,x,G)\;{\longrightarrow}\;{\sigma}(X,x,G)$ is open for each $x{\in}X$, then ${\lambda}$ induces a homeomorphism between the fundamental groups ${\sigma}(X,x_0,G)$ and ${\sigma}(X,y_0,G)$ where ${\lambda}$ is a path from $x_0$ to $y_0$ in X ; The space ${\sigma}(X,x_0,G)$ is an H-space if the identification map $p:{\Sigma}(X,x_0,G)\;{\longrightarrow}\;{\sigma}(X,x_0,G)$ is open in a topological transformation group (X, G, ${\pi}$).

• East Asian mathematical journal
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• 제25권4호
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• pp.433-440
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• 2009

Let R be a ring with unity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will consider some group actions on X by G, the left (resp. right) regular action and the conjugate action. In this paper, by investigating these group actions we can have some results as follows: First, if E(R), the set of all nonzero nonunit idempotents of a unit-regular ring R, is commuting, then $o_{\ell}(x)\;=\;o_r(x)$, $o_c(x)\;=\;\{x\}$ for all $x\;{\in}\;X$ where $o_{\ell}(x)$ (resp. $o_r(x)$, $o_c(x)$) is the orbit of x under the left regular (resp. right regular, conjugate) action on X by G and R is abelian regular. Secondly, if R is a unit-regular ring with unity 1 such that G is a cyclic group and $2\;=\;1\;+\;1\;{\in}\;G$, then G is a finite group. Finally, if R is an abelian regular ring such that G is an abelian group, then R is a commutative ring.

• 대한의생명과학회지
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• 제3권1호
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• pp.21-28
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• 1997

S-2 (3-aminopropylamino)ethylphosphorothioic acid (WR-2721)이 방사선에 대한 방어 효과에 미치는 영향을 규명 하고자 Sprague-Dawley계 웅성 흰쥐를 대조군, WR-2721 단독투여 군 (200mg/kg), X-선 단독조사군, WR-2721투여 (200mg/kg)후 X-선 조사한 병용군으로 나누어 X-선 8 Gy선량을 전신 조사한 후 1, 3, 7, 10일 간에 각각 혈액을 채취하여 효소활성 치와 glucose함량 변화를 측정하여 다음과 같은 결과를 얻었다. X-선 단독조사군에서는 ALP와 AST의 활성치가 대조군에 비하여 감소하였으나 WR-2721을 병용한 군에서는 그 감소폭이 줄어들었고, ALT와 LDH의 활성치는 X-선 단독조사군에서 대조군에 비하여 증가하였고, WR-2721을 병용한 군에서는 그 증가폭이 감소되었다. 또한 glucose치의 변동은 X-선 단독 조사군에서 대조군에 비하여 유의성 있게 증가하였으나 WR-2721을 병용한 군에서는 그 증가폭이 감소되었다. 이로 미루어 보아 WR-2721이 X-선으로부터 생체내 주요 장기들을 보호하는 작용이 있음을 시사하고 있다.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.75-96
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• 2006

Let m, n be positive integers. We denote by R(m,n) (respectively P(m,n)) the class of all groups G such that, for every n subsets $X_1,X_2\ldots,X_n$, of size m of G there exits a non-identity permutation $\sigma$ such that $X_1X_2{\cdots}X_n{\cap}X_{\sigma(1)}X_{/sigma(2)}{\cdots}X_{/sigma(n)}\neq\phi$ (respectively $X_1X_2{\cdots}X_n=X_{/sigma(1)}X_{\sigma(2)}{\cdots}X_{\sigma(n)}$). Let G be a non-abelian group. In this paper we prove that (i) $G{\in}P$(2,3) if and only if G isomorphic to $S_3$, where $S_n$ is the symmetric group on n letters. (ii) $G{\in}R$(2, 2) if and only if ${\mid}G{\mid}\geq8$. (iii) If G is finite, then $G{\in}R$(3, 2) if and only if ${\mid}G{\mid}\geq14$ or G is isomorphic to one of the following: SmallGroup(16, i), $i\in$ {3, 4, 6, 11, 12, 13}, SmallGroup(32, 49), SmallGroup(32, 50), where SmallGroup(m, n) is the nth group of order m in the GAP [13] library.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.227-232
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• 2006

We study some dynamical properties in the context of bitransformation groups, and show that if (H,X,T) is a bitransformation group such that (H,X) is almost periodic and (X/H,T) is pointwise almost periodic $T_2$ and $x{\in}X$, then $E_x=\{q{\in}E(H,X){\mid}qx{\in}{\overline{xT}\}$ is a compact $T_2$ topological group and $E_{qx}=E_x(q{\in}E(H,X))$ when H is abelian, where E(H,X) is the enveloping semigroup of the transformation group (H,X).

• 대한수학회보
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• 제33권2호
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• pp.253-258
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• 1996

Let X be a finite connected CW-complex, $\Gamma = \pi_1(X)$ its fundamental group, $\tilde{X}$ its universal covering space. Then $\Gamma$ acts on $\tilde{X}$ by covering transformations and on the homology group $H_*(\tilde{X})$. In this note we establish the following vanishing result for the Euler characteristic $x(X)$ of X.

• 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.

• 대한수학회보
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• 제30권1호
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• pp.53-59
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• 1993

In this paper, we want to find a subgroup HJ(f, $x_{0}$, G) of the extended Jiang subgroup of a transformation group which is contained in Z( $f_{\sigma}$(.sigma.(X, $x_{0}$, G)), .sigma.(X, f( $x_{0}$), G)) and is an extension of the Jiang subgroup J(f, $x_{0}$). This is, if the acting group G is the trivial group {1x}, then this is the Jiang's results.ults..ults.