Normal Subgroups in Free Burnside Groups of Odd Period

Normal Subgroups in Free Burnside Groups of Odd Period

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In the current paper we announce a positive answer for all prime numbers $n > 997$ to the following problem set by Adian in Kourovka Notebook: Is it true that all proper normal subgroups of the group $B(m, n)$ of prime period $n > 665$ are not free periodic groups? The current result also str...

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Main Author: Varujan Atabekyan
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2008-10-01
Series:Armenian Journal of Mathematics
Online Access:http://test.armjmath.sci.am/index.php/ajm/article/view/24
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spelling doaj-14890254fe754626ab9c7ba5a653b62f2020-11-24T21:58:32ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632008-10-0112Normal Subgroups in Free Burnside Groups of Odd PeriodVarujan Atabekyan0Yerevan State University, Yerevan, Armenia In the current paper we announce a positive answer for all prime numbers $n > 997$ to the following problem set by Adian in Kourovka Notebook: Is it true that all proper normal subgroups of the group $B(m, n)$ of prime period $n > 665$ are not free periodic groups? The current result also strengthens a similar result of Olshanskiy for sufficiently large odd numbers $n$ ($n > 10^{77}$). http://test.armjmath.sci.am/index.php/ajm/article/view/24
collection DOAJ
language English
format Article
sources DOAJ
author Varujan Atabekyan
spellingShingle Varujan Atabekyan
Normal Subgroups in Free Burnside Groups of Odd Period
Armenian Journal of Mathematics
author_facet Varujan Atabekyan
author_sort Varujan Atabekyan
title Normal Subgroups in Free Burnside Groups of Odd Period
title_short Normal Subgroups in Free Burnside Groups of Odd Period
title_full Normal Subgroups in Free Burnside Groups of Odd Period
title_fullStr Normal Subgroups in Free Burnside Groups of Odd Period
title_full_unstemmed Normal Subgroups in Free Burnside Groups of Odd Period
title_sort normal subgroups in free burnside groups of odd period
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2008-10-01
description In the current paper we announce a positive answer for all prime numbers $n > 997$ to the following problem set by Adian in Kourovka Notebook: Is it true that all proper normal subgroups of the group $B(m, n)$ of prime period $n > 665$ are not free periodic groups? The current result also strengthens a similar result of Olshanskiy for sufficiently large odd numbers $n$ ($n > 10^{77}$).
url http://test.armjmath.sci.am/index.php/ajm/article/view/24
work_keys_str_mv AT varujanatabekyan normalsubgroupsinfreeburnsidegroupsofoddperiod
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