We consider a factorized group G=AB where A and B are subgroups of G. We introduce the concept of (A, B, X) -orbit of an element of G and we study the relation between the (A, B, X) -orbit of an element and the element itself; our main result relates the cardinality of the (A, B, X) -orbit of an element of G to the order of the element.
Some observations on factorized groups
BUSETTO, Giorgio;JABARA, Enrico
2006-01-01
Abstract
We consider a factorized group G=AB where A and B are subgroups of G. We introduce the concept of (A, B, X) -orbit of an element of G and we study the relation between the (A, B, X) -orbit of an element and the element itself; our main result relates the cardinality of the (A, B, X) -orbit of an element of G to the order of the element.
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