Transitive and fully transitive groups

Citations Over Time

Abstract

The notions of transitivity and full transitivity for abelian $p$-groups were introduced by Kaplansky in the 1950s. Important classes of transitive and fully transitive $p$-groups were discovered by Hill, among others. Since a 1976 paper by Corner, it has been known that the two properties are independent of one another. We examine how the formation of direct sums of $p$-groups affects transitivity and full transitivity. In so doing, we uncover a far-reaching class of $p$-groups for which transitivity and full transitivity are equivalent. This result sheds light on the relationship between the two properties for all $p$-groups.

Related Papers

• An algorithm to compute the transitive closure, a transitive approximation and a transitive opening of a fuzzy proximity(2009)
• → Computing a Transitive Opening of a Reflexive and Symmetric Fuzzy Relation(2005)4 cited
• Research on Judging a Transitive Bbinary-Relation(2008)
• Research on the incremental updating of the transitive closure(2015)
• On Transitivity and Transitive Closure for Binary Relation(2004)