主 题: Burnside problem on periodic groups and related topics
报告人: Prof. S.I.Adian (俄罗斯科学院 院士)
时 间: 2006-11-03 下午 2:30 - 3:30
地 点: 理科一号楼 1114(数学所活动)
Fix n≥2 and consider the group
G=<a1,…,am∣Xn =1>
with the identity Xn =1. Is the group G finite?
In the monograph devoted to combinatorial group theory, Prof.Wilhelm Magnus has characterised the ABurnside problem as follows:
Very much like Fermats Last Theorm in number theory, Burnsides problem has acted as a catalyst for research in group theory. The fascination exerted by a problem with an extremely simple formulation which then truns ot to be extremely difficult has something irresistible about to the mind of the mathematician.
A negative solution of the Burnside problem on periodic groups was given in joint works by P.S.Novikv and S.I.Adian published in [1968]. The authors proved in 1968 the infiniteness of free perildic groups B(m,n) for all exponents n=kl with odd k≥4381 and m>1 generators.
For a solution of the Burnside problem in [1968] novikov and Adian created a new method based on a classification of periodic words and a corresponding system of defining relations for the group B(m,n) by simultaneous induction on a natural parameter α called rank.
Investigations of periodic groups and a solution of many other old complicated problems in the group theory on the base of modifications of Novikov-Adian method were continued during the last 40 years by S.I.Adian, His students and successors.
A survey of these results will be given in the talk.
defining relations for the group B(m,n) by simultaneous induction on a natural parameter α called rank.
Investigations of periodic groups and a solution of many other old complicated problems in the group theory on the base of modifications of Novikov-Adian method were continued during the last 40 years by S.I.Adian, His students and successors.
A survey of these results will be given in the talk.
