Lectures on Abelian Groups1936 - Abelian groups - 58 pages |
Common terms and phrases
ABELIAN GROUPS additive group basis of J(i classes of J(R+)/J complete group complete subgroup completes the proof contained in J(X continuum of elements Corollary countable groups direct sum direct summand element of finite element of lowest elements b(j exist elements exists a basis exists an element F-J-group finite number finite order finite rank follows that J(R form an ordered Furthermore greatest linearly independent group F group of rational groups isomorphic groups of rank groups Z(v Hence indecomposable group induction infinite cyclic group intersection invariant isomorphic groups J(L+ J(R+ let n(p linearly independent subset lowest type minimal-type mod pJ number of elements number of groups number q ordered set p-complete prove our statement R₁ rational numbers REINHOLD BAER rx exists satisfies the conditions smallest closed subgroup sufficient to prove sum of groups sum of isomorphic summands of rank Suppose Theorem type R type type R₂ types R(i