Abstract:
We prove the finiteness of any abelian subgroup of a free periodic group of odd order n⩾4381. We also show that for these groups the conjugacy problem is solvable.
Citation:
P. S. Novikov, S. I. Adian, “On abelian subgroups and the conjugacy problem in free periodic
groups of odd order”, Math. USSR-Izv., 2:5 (1968), 1131–1144
\Bibitem{NovAdi68}
\by P.~S.~Novikov, S.~I.~Adian
\paper On abelian subgroups and the conjugacy problem in free periodic
groups of odd order
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1131--1144
\mathnet{http://mi.mathnet.ru/eng/im2512}
\crossref{https://doi.org/10.1070/IM1968v002n05ABEH000722}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=233876}
\zmath{https://zbmath.org/?q=an:0204.34102}
Linking options:
https://www.mathnet.ru/eng/im2512
https://doi.org/10.1070/IM1968v002n05ABEH000722
https://www.mathnet.ru/eng/im/v32/i5/p1176
This publication is cited in the following 22 articles:
V. S. Atabekyan, L. D. Beklemishev, V. S. Guba, I. G. Lysenok, A. A. Razborov, A. L. Semenov, “Questions in algebra and mathematical logic. Scientific heritage of S. I. Adian”, Russian Math. Surveys, 76:1 (2021), 1–27
S. I. Adian, “New estimates of odd exponents of infinite Burnside groups”, Proc. Steklov Inst. Math., 289 (2015), 33–71
V. S. Atabekyan, “Normal automorphisms of free Burnside groups”, Izv. Math., 75:2 (2011), 223–237
V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24
S. I. Adian, “The Burnside problem and related topics”, Russian Math. Surveys, 65:5 (2010), 805–855
V. S. Atabekyan, “The normalizers of free subgroups in free Burnside groups of odd period $n\ge1003$”, J. Math. Sci., 166:6 (2010), 691–703
L. D. Beklemishev, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, M. R. Pentus, A. A. Razborov, A. L. Semenov, V. A. Uspenskii, “Sergei Ivanovich Adian (on his 75th birthday)”, Russian Math. Surveys, 61:3 (2006), 575–588
V. I. Senashov, A. I. Sozutov, V. P. Shunkov, “Investigation of groups with finiteness conditions in Krasnoyarsk”, Russian Math. Surveys, 60:5 (2005), 805–848
S. I. Adian, “The Burnside Problem on Periodic Groups, and Related Problems”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S2–S12
S. I. Adian, V. G. Durnev, “Decision problems for groups and semigroups”, Russian Math. Surveys, 55:2 (2000), 207–296
V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182
S. I. Adian, “An axiomatic method of constructing groups with given properties”, Russian Math. Surveys, 32:1 (1977), 1–14
V. P. Shunkov, “On Abelian subgroups in biprimitively finite groups”, Algebr Logic, 12:5 (1973), 347
S.I. Adjan, Studies in Logic and the Foundations of Mathematics, 71, Word Problems - Decision Problems and the Burnside Problem in Group Theory, 1973, 19
S. N. Chernikov, “Shmidt's investigations in the theory of infinite groups”, Ukr Math J, 23:5 (1972), 487
D. I. Zaitsev, M. I. Kargapolov, V. S. Charin, “Infinite groups with specified properties of subgroups”, Ukr Math J, 24:5 (1972), 497
V. P. Shunkov, “On periodic groups with an almost regular involution”, Algebr Logic, 11:4 (1972), 260
S. N. Chernikov, “On Shmidt's problem”, Ukr Math J, 23:5 (1972), 493
S. I. Adian, “On some torsion-free groups”, Math. USSR-Izv., 5:3 (1971), 475–484
V. P. Shunkov, “On the minimality property for locally finite groups”, Algebr Logic, 9:2 (1970), 137
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