Results 1 
3 of
3
A NOTE ON FINITE CTIDY GROUPS
, 2013
"... Let G be a group and x ∈ G. The cyclicizer of x is defined to be the subset Cyc(x) = {y ∈ G  〈x, y 〉 is cyclic}. G is said to be a tidy group if Cyc(x) is a subgroup for all x ∈ G. We call G to be a Ctidy group if Cyc(x) is a cyclic subgroup for all x ∈ G \K(G), where K(G) is the intersection of ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Let G be a group and x ∈ G. The cyclicizer of x is defined to be the subset Cyc(x) = {y ∈ G  〈x, y 〉 is cyclic}. G is said to be a tidy group if Cyc(x) is a subgroup for all x ∈ G. We call G to be a Ctidy group if Cyc(x) is a cyclic subgroup for all x ∈ G \K(G), where K(G) is the intersection of all the cyclicizers in G. In this note, we classify finite Ctidy groups with K(G) = {1}.