Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Intersections of $ \Gamma $-isotype subgroups in abelian groups


Author: Jindřich Bečvář
Journal: Proc. Amer. Math. Soc. 86 (1982), 199-204
MSC: Primary 20K21
DOI: https://doi.org/10.1090/S0002-9939-1982-0667272-9
MathSciNet review: 667272
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A subgroup $ H$ of an abelian group $ G$ is an intersection of isotype subgroups of $ G$ if and only if, for each prime $ p$, if $ x + H$ is a coset of order $ p$ then there is another coset of order $ p$ containing an element $ y$ of order $ p$ such that $ h_p^* (x) \leqslant h_p^*(y)$. A subgroup $ H$ of $ G$ is isotype in $ G$ if and only if, for each prime $ p$, every coset $ x + H$ of order $ p$ contains an element y of order $ p$ such that $ h_p^*(x)h_p^*(y)$


References [Enhancements On Off] (What's this?)

  • [1] D. Boyer and K. M. Rangaswamy, Intersections of pure subgroups in abelian groups, Proc. Amer. Math. Soc. 81 (1981), 178-180. MR 593451 (82b:20076)
  • [2] B. Charles, Une caractérisation des intersections de sous-groups divisibles, C. R. Acad. Sci. Paris Sér. A-B 250 (1960), 256-257. MR 0109176 (22:64)
  • [3] L. Fuchs, Infinite abelian groups. I, II, Academic Press, New York, 1970, 1973.
  • [4] -, Review of [2], Math. Rev. 22 (1961), 10-11.
  • [5] -, Recent results and problems on abelian groups, Topics in Abelian Groups, Scott, Foresman & Co., Glenview, Ill., 1963, pp. 9-40. MR 0169906 (30:149)
  • [6] C. Megibben, On subgroups of primary abelian groups, Publ. Math. Debrecen 12 (1965), 293-294. MR 0186732 (32:4190)
  • [7] K. M. Rangaswamy, Characterization of intersections of neat subgroups of abelian groups, J. Indian Math. Soc. 29 (1965), 31-36. MR 0183778 (32:1255)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20K21

Retrieve articles in all journals with MSC: 20K21


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0667272-9
Keywords: Abelian groups, isotype, $ \Gamma $-isotype subgroups
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society