Forum Problem Lists Definitions FAQ

7.1 (1980)

Solved

The free periodic groups $B(m, p)$ of prime exponent $p > 665$ are known to possess many properties similar to those of absolutely free groups (see S. I. Adian, The Burnside Problem and Identities in Groups, Springer, Berlin, 1979). Is it true that all normal subgroups of $B(m, p)$ are not free periodic groups?

Contributor: S. I. Adian

Progress

Yes, it is true for all sufficiently large $p$ (A. Yu. Olshanskii, in: Groups, rings, Lie and Hopf algebras, Int. Workshop, Canada, 2001, Dordrecht, Kluwer, 2003, 179–187); this is also proved for all primes $p \geqslant 1003$ (V. S. Atabekyan, Fund. Prikl. Mat., 15, no. 1 (2009), 3–21 (Russian)).

Comments

All comments are the responsibility of the user. Comments appearing on this page are not verified for correctness. Please keep posts mathematical and on topic. If you want to submit a proof (or a partial proof), please use the dedicated proof submission form rather than posting it in the comments.
Order by newest first or oldest first.

No comments yet. Be the first to comment.

Proof claims

Proof claims are the responsibility of the submitter. Appearance here does not mean the claim has been checked for mathematical correctness. Moderators only screen for spam, abuse, and obviously low-effort submissions.

No proof claims yet.