电邮这篇文章 Free products of groups are strongly verbally closed
- 作者: Mazhuga A.M.1
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隶属关系:
- Faculty of Computer Science, National Research University "Higher School of Economics"
- 期: 卷 210, 编号 10 (2019)
- 页面: 122-160
- 栏目: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/133292
- DOI: https://doi.org/10.4213/sm9115
- ID: 133292
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详细
In a number of recent papers it was established that many almost free groups, fundamental groups of almost all connected surfaces, and all groups that are nontrivial free products of groups with identities are algebraically closed in any group in which they are verbally closed. In the present paper we establish that any group that is a nontrivial free product of groups is algebraically closed in any group in which it is verbally closed. Bibliography: 13 titles.
作者简介
Andrey Mazhuga
Faculty of Computer Science, National Research University "Higher School of Economics"
Email: mazhuga.andrew@yandex.ru
Candidate of physico-mathematical sciences, no status
参考
- A. G. Myasnikov, V. Roman'kov, “Verbally closed subgroups of free groups”, J. Group Theory, 17:1 (2014), 29–40
- V. Roman'kov, “Equations over groups”, Groups Complex. Cryptol., 4:2 (2012), 191–239
- В. А. Романьков, Н. Г. Хисамиев, “Вербально и экзистенциально замкнутые подгруппы свободных нильпотентных групп”, Алгебра и логика, 52:4 (2013), 502–525
- Ант. А. Клячко, А. М. Мажуга, “Вербально замкнутые почти свободные подгруппы”, Матем. сб., 209:6 (2018), 75–82
- A. M. Mazhuga, “On free decompositions of verbally closed subgroups in free products of finite groups”, J. Group Theory, 20:5 (2017), 971–986
- A. M. Mazhuga, “Strongly verbally closed groups”, J. Algebra, 493:1 (2018), 171–184
- A. A. Klyachko, A. M. Mazhuga, V. Y. Miroshnichenko, “Virtually free finite-normal-subgroup-free groups are strongly verbally closed”, J. Algebra, 510 (2018), 319–330
- Ж.-П. Серр, “Деревья, амальгамы и ${SL}_2$”, Математика, 18:1 (1974), 3–51
- P. de la Harpe, Topics in geometric group theory, Chicago Lectures in Math., Univ. of Chicago Press, Chicago, IL, 2000, vi+310 pp.
- N. J. Fine, H. S. Wilf, “Uniqueness theorems for periodic functions”, Proc. Amer. Math. Soc., 16 (1965), 109–114
- А. Г. Курош, Теория групп, 3-е изд., Наука, М., 1967, 648 с.
- И. А. Грушко, “О базисах свободного произведения групп”, Матем. сб., 8(50):1 (1940), 169–182
- S. V. Ivanov, “On certain elements of free groups”, J. Algebra, 204:2 (1998), 394–405
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