Normal Subgroups in Free BurnsideGroups of Odd Period

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Normal Subgroups in Free BurnsideGroups of Odd Period Varujan Atabekyan

In the current paper we announce a positive answerfor all prime numbersn>997 to the following problem set byAdian in Kourovka Notebook: Is it true that all proper normal sub-groups of the groupB(m,n) of prime periodn>665 are not freeperiodic groups? The current result also strengthens a similar re-sult of Olshanskiy for sufficiently large odd numbers n (n>1077).

DOI: https://armjmath.sci.am/index.php/ajm/article/view/24 Armenian Journal of MathematicsVolume 1, Number 2 25–29

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Keywords

Burnside groups, normalizer of subgroup, variety ofn-periodic groups, non-abelian simple group

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