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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2004.1
- 수록면
- 21 - 29 (9page)
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Suppose G is an abelian group with p-primary component Gp and F is a field of charF = p > 0. The main goal, motivating the present paper, is to show that if G is a direct sum of groups whose p-components are of countable lengths direct sums of countable groups, then Gp is a direct factor of the groupS(FG) of all normed p-units in the group algebra FG with a direct sum of countables complementary factor or equivalently S(FG)=Gp is a direct sum of countables. In particular, when G is p-mixed, it is proved that G is a direct factor of the groupV(FG) of all normalized units in FG with a direct sum of p-countables complementary factor or in other words V(FG)=G is a direct sum of p-countables. Moreover, for an arbitrary group H the F-isomorphism FH = FG implies that Hp = Gp, and that there exists a direct sum of p-countables T with the property that H T = G T provided G is p-mixed.These facts on the group structure and on the isomorphism problem generalize statements due to Hill-Ullery (Commun. Algebra, 1997) and to the author (Compt. rend.Acad. bulg. Sci., 1995 and Hokkaido Math. J., 2000). Besides, the claims on the isomorphism partially settle a question raised by May (Proc. Amer. Math. Soc., 1988) and extend an other author's result in this theme (Proc. Amer. Math. Soc., 1997).
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참고문헌 (12)
참고문헌 신청
/ / The solution to W. May's problem for isomorphism of commutative groupalgebras of mixed groups over ？
/ 1988 / Proc. Amer.Math. Soc. 104 2 : 403 ~ 409
/ 1989 / Unit Groups of Group Rings amsterdam
/ 1992 / Commun. Algebra 20 9 : 655 ~ 664
/ 1995 / Topologically pure^basis subgroups in commutative group rings 48 (9-10) : 7 ~ 10
/ 1988 / Proc. Amer.Math. Soc. 104 2 : 403 ~ 409
/ 1989 / Unit Groups of Group Rings amsterdam
/ 1992 / Commun. Algebra 20 9 : 655 ~ 664
/ 1995 / Topologically pure^basis subgroups in commutative group rings 48 (9-10) : 7 ~ 10
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