Natural Sciences, Mathematics, 2026
Normal Subgroups in Free BurnsideGroups of Odd Period
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Submitted: 2024-11-29
© 2026 by author(s) and The Gufo Inc.
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Abstract
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).