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Permutations which make transitive groups primitive

Pedro Lopes (2009)

Open Mathematics

In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive groups...

Plane trivalent trees and their patterns

Charles Delorme (2010)

Open Mathematics

The aim of this paper is to characterize the patterns of successive distances of leaves in plane trivalent trees, and give a very short characterization of their parity pattern. Besides, we count how many trees satisfy some given sequences of patterns.

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