Electronic Resource
Springer
Periodica mathematica Hungarica
40 (2000), S. 205-209
ISSN:
1588-2829
Keywords:
Finite group
;
small square property
;
exact square property
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let G be a finite group written multiplicatively and k a positive integer. If X is a non-empty subset of G, write X 2 = |xy | x, y ∈ X . We say that G has the small square property on k-sets if |X 2| 〈 k 2 for any k-element subset X of G. For each group G, there is a unique m = m G such that G has the small square property on (m + 1)-sets but not on m-sets. In this paper we show that given any positive integer d, there is a finite group G with m G = d.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1010395728145
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