Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-15T01:51:46.598Z Has data issue: false hasContentIssue false
  • English
  • Français

General Products of Two Finite Cyclic Groups

Published online by Cambridge University Press:  18 May 2009

K. R. Yacoub
K. R. Yacoub
Affiliation:
Faculty of Science, University Of Alexandria, Egypt.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Groups that can be represented as the product of two proper subgroups have been studied extensively; one of the latest contributions is a paper by Wielandt (8), in which references to previous work can be found. In the case where the two proper subgroups have only the unit element in common, we adopt the term ‘general product’introduced by Neumann (1).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 2 , Issue 3 , July 1955 , pp. 116 - 123
Copyright
Copyright © Glasgow Mathematical Journal Trust 1955

References

REFERENCES

(1)Neumann, B. H., ‘Decomposition of Groups, J. London Math. Soc., 10 (1935), 3–6.Google Scholar
(2)Zappa, G., ‘Sulla costrazione dei gruppi prodotto di due dati sottogruppi permutabili tra loro’, Atti Secondo Congresso Un. Mat. Ital. Bologna (1940), 119–125.Google Scholar
(3)Ródei, L., ‘Zur Theorie der faktorisierbaren Gruppen I’, Acta Math. Acad. Sci. Hungar. 1 (1950), 74–98.CrossRefGoogle Scholar
(4)Douglas, J., On Finite Groups with Two Independent Generators, Proc. Nat. Acad. Sci. U.S.A., 37 (1951), 604–610.CrossRefGoogle ScholarPubMed
(5)Douglas, J., ‘On Finite Groups with Two Independent Generators, Proc. Nat. Acad. Sci. U.S.A., 37 (1951), 677–691.CrossRefGoogle ScholarPubMed
(6)Douglas, J., On Finite Groups with Two Independent Generators. Exponential Substitutions’, Proc. Nat. Acad. Sci. U.S.A., 37 (1951), 749–760.CrossRefGoogle ScholarPubMed
(7)Douglas, J., On Finite Groups with Two Independent Generators. Conjugate Substitutions’, Proc. Nat. Acad. Sci. U.S.A., 37 (1951), 808–813.CrossRefGoogle ScholarPubMed
(8)Wielandt, H., Über das Product paarweise vertauschbarer nilpotenter Gruppen’, Math. Zeit. 55 (1951), 1–7.CrossRefGoogle Scholar