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

Abundance of progression in large set for non commutative semigroup