ID  33221 
FullText URL  
Author 
Danchev, Peter

Abstract  Let F be a field of char(F) = p > 0 and G an abelian group with pcomponent G_{p} of cardinality at most ℵ_{1} and length at most ω_{1}. The main affirmation on the Direct Factor Problem is that S(FG)/G_{p} is totally projective whenever F is perfect. This extends results due to May (Contemp. Math., 1989) and HillUllery (Proc. Amer. Math. Soc., 1990). As applications to the Isomorphism Problem, suppose that for any group H the Fisomorphism FH ≅ FG holds. Then if G_{p} is totally projective, H_{p} ≅ G_{p}. This partially solves a problem posed by May (Proc. Amer. Math. Soc., 1988). In particular, H ≅ G provided G is pmixed of torsionfree rank one so that G_{p} is totally projective. The same isomorphism H ≅ G is fulfilled when G is plocal algebraically compact too. Besides if F_{p} is the simple field with pelements and G_{p} F_{p}H is a coproduct of torsion complete groups, F_{p}H ≅ F_{p}G as F_{p} F_{p}algebras implies H_{p} ≅ G_{p}. This expands the central theorem obtained by us in (Rend. Sem. Mat. Univ. Padova, 1999) and partly settles the generalized version of a question raised by May (Proc. Amer. Math. Soc.,1979) as well. As a consequence, when G_{p} is torsion complete and G is pmixed of torsionfree rank one, H ≅ G. Moreover, if G is a coproduct of plocal algebraically compact groups then H ≅ G. The last attainment enlarges an assertion of BeersRichmanWalker (Rend. Sem. Mat. Univ. Padova, 1983). Each of the reported achievements strengthens our statements in this direction (Southeast Asian Bull. Math., 20012002) and also continues own studies in this aspect (Hokkaido Math. J., 2000) and (Kyungpook Math. J., 2004). 
Published Date  200901

Publication Title 
Mathematical Journal of Okayama University

Volume  volume51

Issue  issue1

Publisher  Department of Mathematics, Faculty of Science, Okayama University

Start Page  179

End Page  192

ISSN  00301566

NCID  AA00723502

Content Type 
Journal Article

language 
英語

File Version  publisher

Refereed 
True

Submission Path  mjou/vol51/iss1/13

JaLCDOI 