News of Science
January 24, 2010

MATHEMATICS;
New mathematics data have been reported by researchers at Yerevan
State University

"We prove that for any odd number n>= 1003, every non-cyclic subgroup
of the 2-generator free Burnside group of exponent. n contains a
subgroup isomorphic to the free Burnside group of exponent n. and
infinite rank," scientists writing in the journal Izvestiya
Mathematics report.

"Various families of relatively free n-periodic subgroups are
constructed in free periodic groups of odd exponent n>= 665," wrote
V.S. Atabekian and colleagues, Yerevan State University.

The researchers concluded: "For the same groups, we describe a
monomorphism tau such that a word A is an elementary period of rank
alpha if and only if its image tau(A) is ail elementary period of rank
alpha + 1."

Atabekian and colleagues published their study in Izvestiya
Mathematics (On subgroups of free Burnside groups of odd exponent n >1003. Izvestiya Mathematics, 2009;73(5):861-892).

Additional information can be obtained by contacting V.S. Atabekian,
Yerevan State University, Yerevan, Armenia.

The publisher of the journal Izvestiya Mathematics can be contacted
at: London Mathematical Society Russian Acad Sciences, C, O Turpion
Ltd, Turpin Distribution Services, Blackhorse Rd., Letchworth SG6 1HN,
Herts, England.