  The notion of abundance of certain type of configuration in certain large
sets was first proved by Furstenberg and Glazner in 1998. After that many
author investigate abundance of different types of configurations in different
types of large sets. Hindman, Hosseini, Strauss and Tootkaboni recently
introduced another notion of large sets called $CR$ sets. Then Debnath and De
proved abundance of arithmetic progression in $CR$ sets for commutative
semigroups. In the present article we investigate abundance of progressions in
for non-commutative semigroups.
