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- W2161269806 abstract "Let F be a field of char(F) = p > 0 and G an abelian group with p-component Gp of cardinality at most @1 and length at most !1. The main affirmation on the Direct Factor Problem is thatS(FG)/Gp is totally projective whenever F is perfect. This extends results due to May (Contemp. Math., 1989) and Hill-Ullery (Proc. Amer. Math. Soc., 1990). As applications to the Isomorphism Problem, suppose that for any group H the F-isomorphism FHFG holds. Then if Gp is totally projective, HpGp. This partially solves a problem posed by May (Proc. Amer. Math. Soc., 1988). In particular, HG provided G is p-mixed of torsion-free rank one so that Gp is totally projective. The same isomorphism HG is fulfilled when G is p-local algebraically compact too. Besides, if Fp is the simple field with p-elements and Gp is a coproduct of torsion complete groups, FpHFpG as Fp-algebras implies HpGp. This expands the central theorem obtained by us in (Rend. Sem. Mat. Univ. Padova, 1999) and partly settles the gener- alized version of a question raised by May (Proc. Amer. Math. Soc., 1979) as well. As a consequence, when Gp is torsion complete and G is p-mixed of torsion-free rank one, HG. Moreover, if G is a co- product of p-local algebraically compact groups then HG. The last attainment enlarges an assertion of Beers-Richman-Walker (Rend. Sem. Mat. Univ. Padova, 1983). Each of the reported achievements strengthens our statements in this direction (Southeast Asian Bull. Math., 2001-2002) and also continues own studies in this aspect (Hokkaido Math. J., 2000) and (Kyungpook Math. J., 2004)." @default.
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- W2161269806 date "2009-01-01" @default.
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- W2161269806 title "COMMUTATIVE GROUP ALGEBRAS OF ABELIAN GROUPS WITH UNCOUNTABLE POWERS AND LENGTHS" @default.
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