Abelian groups and $\Re$-semigroups
نویسندگان
چکیده
منابع مشابه
non-divisibility for abelian groups
Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
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ly we know that 〈A 〉 always exists since 〈A 〉 = ⋂ {H ⊆ G | A ⊆ H subgroup } But computationally this is useless: we already have to know all subgroups (containing A) to compute the intersection. Even if G is finite and relatively small, there is no hope to build an algorithm on this characterization. Also note that 〈A 〉 is one of the H’s on the right hand side (impredicative definition). So how...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1970
ISSN: 0386-2194
DOI: 10.3792/pja/1195520391