This progress is categorised by both periodic group and special topics.

Burnside's problem asks whether, conversely, any finitely generated periodic group must be finite.

PlanetMath articles on periodic groups and exponent.

One of the interesting properties of periodic groups is that they cannot be formalized in terms of first-order logic.

But with the discovery of helium, neon, krypton, xenon and finally radon, it was clear that they formed a perfect periodic group.

Because of user non-participation, factionalism and the failure of user committees, periodic group meetings were organised by staff.

There exist easily defined groups such as the p-group which are infinite periodic groups; but the latter group cannot be finitely generated.

In group theory, a periodic group or a torsion group is a group in which each element has finite order.

Since all locally finite groups are periodic, this means that for linear groups and periodic groups the conditions are identical.

The referees are brought together for periodic group workouts, then are assigned a "remote trainer" who assigns them daily exercises - weights, sprints, endurance runs.

The concept of a periodic group should not be confused with that of a cyclic group, although all finite cyclic groups are periodic.

Burnside's problem is a classical question, which deals with the relationship between periodic groups and finite groups, if we assume only that G is a finitely-generated group.

R. I. Grigorchuk, On Burnside's problem on periodic groups, Functional Anal.

Supports two methods of denormalization: repeating groups in a record ("periodic groups"); and multiple value fields in a record ("multi-value fields").

S. V. Aleshin, Finite automata and the Burnside problem for periodic groups, (Russian) Mat.

Several of those who have been discouraged by watching the President's popularity slide have formed an informal support network in Washington, and some join in periodic group dinners.

Explicit examples of finitely generated infinite periodic groups were constructed by Golod, based on joint work with Shafarevich, and by Aleshin and Grigorchuk using automata.

These ideas are alternated and juxtaposed, and finally resolved in the appearance of a new texture of irregularly spaced fast periodic groups in the upper register (Smalley 1969, 31-32).

The structure of general infinite abelian groups can be considerably more complicated and the conclusion needs not to hold, but Prüfer proved that it remains true for periodic groups in two special cases.

In mathematics, given a prime number p, a p-group is a periodic group in which each element has a power of p as its order: each element is of prime power order.

A finitely generated periodic group must be finite if it is boundedly generated; equivalently, an infinite finitely generated periodic group is not boundedly generated.

To show that no (non-cyclic) free group has bounded generation, it is therefore enough to produce one example of a finitely generated group which is not boundedly generated, and any finitely generated infinite periodic group will work.

Examples of infinite periodic groups include the additive group of the ring of polynomials over a finite field, and the quotient group of the rationals by the integers, as well as their direct summands, the Prüfer groups.

Issai Schur had showed in 1911 that any finitely generated periodic group that was a subgroup of the group of invertible n x n complex matrices was finite; he used this theorem to prove the Jordan-Schur theorem.

In particular, a stratified version of small cancellation theory, developed by Ol'shanskii, resulted in constructions of various group-theoretic "monsters", such as the Tarski Monster, and in geometric solutions of the Burnside problem for periodic groups of large exponent.