Related papers: The Tits Alternative: An Elementary Exposition

This paper has been withdrawn by the author.

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 The paper is withdrawn until further notice.

This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

Major mistake. The paper has been withdrawn.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

This paper has being withdrawn by the authors due to an error in the conclusion.

The paper was withdrawn because of its significant overlap with a paper appeared recently.

This paper has been withdrawn by the author, due to the insecurity against attacks received in quant-ph/0605027v5.

This paper has been withdrawn by the author due to its main result being included in cond-mat/0403309 by the same author.

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the authors due to the crucial wrong assumption following Eq. 9.

This paper has been withdrawn by the author. There is an error on page 3 in the last inequality before Lemma 1.1.

The paper has been withdrawn due to an error in the main theorem.

This paper has been withdrawn by the author(s), due a crucial sign error in Eqn. 1.

This paper is wrong and is therefore withdrawn.

This paper has been withdrawn by the author, due to errors in the figures.

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.

%auto-ignore This paper has been withdrawn by the author, due to a crucial error.

This paper has been withdrawn by the authors, due a crucial error in Sec. 3.