IJPAM: Volume 106, No. 1 (2016)
THE ACTION OF THE ALTERNATING GROUP
ON UNORDERED SUBSETS
Pure and Applied Mathematics Department
Jomo Kenyatta University of Agriculture and Technology
P.O. Box 62000-00200, Nairobi, KENYA
P.O. Box 43844-00100, Nairobi, KENYA
Abstract. The transitivity, primitivity, rank and subdegrees, as well as pairing of the suborbits associated with the action of the alternating group , on unordered element subsets of a set of letters, have not received any attention. In this paper, we prove that this action is transitive. We also show that the action is imprimitive if and only if . In addition, we establish that the rank associated with the action is a constant if and only if , except for in which case the rank is 4 if , but is 3 for all . Further, we calculate the subdegrees associated with the action and arrange them according to their increasing magnitudes. Finally, we show that all the suborbits of the action, with the exception of some non-trivial suborbits corresponding to the actions of and on the set of unordered pairs, are self-paired.
Received: September 21, 2015
AMS Subject Classification: 05E18
Key Words and Phrases: alternating group, action, rank, subdegrees, unordered element subset, suborbit
Download paper from here.
DOI: 10.12732/ijpam.v106i1.27 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 333 - 346