The equivalence of $\times ^{t}C\approx \times ^{t}D$ and $J\times C\approx J\times D$
HTML articles powered by AMS MathViewer
- by Ronald Hirshon PDF
- Trans. Amer. Math. Soc. 249 (1979), 331-340 Request permission
Abstract:
Let C satisfy the maximal condition for normal subgroups and let $\times { ^t}C \approx \times { ^t}D$ for some positive integer t. Then $C \times J \approx D \times J$ where J is the infinite cyclic group. If $\times { ^s}C \approx \times { ^t}D$ and $s \geqslant t$, there exists a finitely generated free abelian group S such that C is a direct factor of $D \times S$.References
- Peter Crawley and Bjarni Jónsson, Refinements for infinite direct decompositions of algebraic systems, Pacific J. Math. 14 (1964), 797–855. MR 169806, DOI 10.2140/pjm.1964.14.797
- P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419–436. MR 72873, DOI 10.1112/plms/s3-4.1.419
- R. Hirshon, Cancellation and Hopficity in direct products, J. Algebra 50 (1978), no. 1, 26–33. MR 463303, DOI 10.1016/0021-8693(78)90171-0
- R. Hirshon, The cancellation of an infinite cyclic group in direct products, Arch. Math. (Basel) 26 (1975), 134–138. MR 376881, DOI 10.1007/BF01229716
- R. Hirshon, Some cancellation theorems with applications to nilpotent groups, J. Austral. Math. Soc. Ser. A 23 (1977), no. 2, 147–165. MR 447410, DOI 10.1017/s1446788700018152
- Ronald Hirshon, The intersection of the subgroups of finite index in some finitely presented groups, Proc. Amer. Math. Soc. 53 (1975), no. 1, 32–36. MR 387417, DOI 10.1090/S0002-9939-1975-0387417-4
- Ronald Hirshon, A conjecture on Hopficity and related results, Arch. Math. (Basel) 22 (1971), 449–455. MR 301103, DOI 10.1007/BF01222603
- J. M. Tyrer Jones, Direct products and the Hopf property, J. Austral. Math. Soc. 17 (1974), 174–196. Collection of articles dedicated to the memory of Hanna Neumann, VI. MR 0349855, DOI 10.1017/S144678870001675X A. G. Kurosh, The theory of groups, Vol. 2, Chelsea, New York, 1966, p. 81.
- D. I. Moldavanskiĭ, Certain subgroups of groups with one defining relation, Sibirsk. Mat. Ž. 8 (1967), 1370–1384 (Russian). MR 0220810
- A. L. Šmel′kin, On the isomorphism of nilpotent decompositions of torsion-free nilpotent groups, Sibirsk. Mat. Ž. 4 (1963), 1412–1425 (Russian). MR 0158008
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 249 (1979), 331-340
- MSC: Primary 20F99
- DOI: https://doi.org/10.1090/S0002-9947-1979-0525676-3
- MathSciNet review: 525676