• Korean Journal of Mathematics
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• v.7 no.1
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• pp.131-138
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• 1999

We introduce an extended Jiang subgroup $J(f,x_0,G)$ of the fundamental group of a transformation group as a generalization of the Jiang subgroup $J(f,x_0)$ and show some properties of this extended Jiang subgroup.

• Korean Journal of Mathematics
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• v.9 no.1
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• pp.61-65
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• 2001

We introduce a subgroup $ HJ(f,x_0,G)$ of the fundamental group of a transformation group as a generalization of the Jiang subgroup $J(f,x_0$) and show some properties of this subgroup.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.609-618
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• 1994

F. Rhodes [2] introduced the fundamental group $\sigma(X, x_0, G)$ of a transformation group (X,G) as a generalization of the fundamental group $\pi_1(X, x_0)$ of a topological space X and showed a sufficient condition for $\sigma(X, x_0, G)$ to be isomorphic to $\pi_1(X, x_0) \times G$, that is, if (G,G) admits a family of preferred paths at e, $\sigma(X, x_0, G)$ is isomorphic to $\pi_1(X, x_0) \times G$. B.J.Jiang [1] introduced the Jiang subgroup $J(f, x_0)$ of the fundamental group of X which depends on f and showed a condition to be $J(f, x_0)$ = Z(f_\pi(\pi_1(X, x_0)), \pi_1(X, f(x_0)))$.

• Korean Journal of Mathematics
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• v.2
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• pp.73-77
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• 1994

• Communications of the Korean Mathematical Society
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• v.6 no.1
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• pp.135-143
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• 1991

• Korean Journal of Mathematics
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• v.1
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• pp.71-83
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• 1993

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.709-715
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• 1997

For a fibration (E,B,p) with fiber F and a fiber map f, we show that if the inclusion $i : F \to E$ has a left homotopy inverse, then $G^f_n(E,F)$ is isomorphic to $G^f_n(F,E) \oplus \pi_n(B)$. In particular, by taking f as the identity map on E we have $G_n(E,F)$ is isomorphic to $G_n(F) \oplus \pi_n(B)$.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.235-244
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• 1996

For a self-map f of a CW-pair (X, A), we introduce the G(f)-sequence of (X, A) which consists of subgroups of homotopy groups in the homotopy sequence of (X, A) and show some properties of the relative homotopy Jian groups. We also show a condition for the G(f)-sequence to be exact.

• Asian Pacific Journal of Cancer Prevention
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• v.14 no.9
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• pp.5483-5487
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• 2013

Background: Associations between Arg399Gln, Arg194Trp and Arg280His polymorphisms of the XRCC1 gene and risk of differentiated thyroid carcinoma (DTC) have been widely studied but the findings are contradictory. Methods: We performed a meta-analysis in the present study using STATA 11.0 software to clarify any associations. Electronic literature databases and reference lists of relevant articles revealed a total of 10, 6 and 6 published studies for the Arg399Gln, Arg194Trp and Arg280His polymorphisms, respectively. Results: No significant associations were observed between Arg399Gln and DTC risk in all genetic models within the overall and subgroup meta-analyses, while the Trp/Trp vs Arg/Arg and recessive model of the Arg194Trp polymorphism was associated with DTC susceptibility, and the dominant model of Arg280His polymorphism contributed to DTC susceptibility in Caucasians. Conclusions: Our meta-analysis suggests that XRCC1 Arg194Trp may be a risk factor for DTC development.