Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-08T04:26:39.903Z Has data issue: false hasContentIssue false
  • English
  • Français

Representation of finite groups as short products of subsets

Published online by Cambridge University Press:  17 April 2009

Xingde Jia
Xingde Jia
Affiliation:
Department of Mathematics SouthwestTexas State University San MarcosTX 78666United States of America
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.

Let M be a finite quasigroup of order n. For any integer k ≥ 2, let H(k, M) be the smallest positive integer h such that there exist h subsets Ai (i = 1, 2, …, h) such that Ai … Ah = M and |Ai| = k for every i = 1, 2, …, h. Define H(k, n) = max H(k, M). It is proved in this paper that

.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 463 - 467
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Babai, L. and Erdös, P., ‘Representation of group elements as short products’, Ann. Discrete Math. 12 (1982), 27–30.Google Scholar
[2]Erdös, P. and Hall, R.R., ‘Probabilistic methods in group theory, II’, Houston J. Math. 2 (1976), 173–185.Google Scholar
[3]Jia, X.-D., ‘Thin bases for finite nilpotent groups’, J. Number Theory 41 (1992), 303–313.CrossRefGoogle Scholar
[4]Jia, X.-D., ‘On a problem of Rohrbach for finite groups’, (preprint).Google Scholar
[5]Kozma, G. and Lev, A., ‘On h−bases and h−decompositions of the finite solvable and alternating groups’, (preprint).Google Scholar
[6]Nathanson, M.B., ‘On a problem of Rohrbach for finite groups’, J. Number Theory 41 (1992), 69–76.Google Scholar
[7]Rohrbach, H., ‘Ein Beitrag zur additiven Zahlentheorie’, Math. Z. 42 (1937), 1–30.CrossRefGoogle Scholar
[8]Rohrbach, H., ‘Anwendung eines Satzes der additiven Zahlentheorie auf eine gruppentheoretische Grage’, Math. Z. 42 (1937), 538–542.Google Scholar