Related papers: Amenability and co-amenability in non-abelian grou…

This paper has been withdrawn by the author because there is a gap in Lemma 9.

This paper has been withdrawn by the author(s) in the light of several other works available and due to a misunderstanding in the authorships.

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

This paper has been withdrawn by the author due to a crucial argument error at p.10.

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.

This paper is withdrawn because of an error in Lemma 3.1

This paper is withdrawn. We found a mistake in Lemma 4.1

This paper has been withdrawn by the authors, due a gap in the proof of the main Theorem.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author due to similarity to Author's other paper

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn by the author due to a gap in the proof of the main result.

This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.

This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2

There have been gaps found in the proofs. The paper is withdrawn until further notice.

This paper has been withdrawn by the author due to an error in the proof of Theorem 1.

This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.

This paper has been withdrawn by the author since the proof of Lemma 8 is not correct.

This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.