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...
متن کاملOn divisibility in definable groups
Let M be an o–minimal expansion of a real closed field. It is known that a definably connected abelian group is divisible. In this note, we show that a definably compact definably connected group is divisible.
متن کاملSome finite groups with divisibility graph containing no triangles
Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $sigma^{ast}(G)=2$, a finite simple group $G$ that satisfies the one-p...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1985
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1985-15335-2