Geodesic
On Zero-divisors in Group Rings of Groups with Torsion
Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 326-334

Voir la notice de l'article provenant de la source Cambridge University Press

Nontrivial pairs of zero-divisors in group rings are introduced and discussed. A problem on the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of odd exponent $n\,\gg \,1$ is solved in the affirmative. Nontrivial pairs of zero-divisors are also found in group rings of free products of groups with torsion.
DOI : 10.4153/CMB-2012-036-6
Mots-clés : 20C07, 20E06, 20F05, 20F50, Burnside groups, free products of groups, group rings, zero-divisors 
Ivanov, S. V.; Mikhailov, Roman. On Zero-divisors in Group Rings of Groups with Torsion. Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 326-334. doi: 10.4153/CMB-2012-036-6
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[1] [1] Cohn, P. M., On the free product of associative rings. II. The case of (skew) fields. Math. Z. 73 (1960, 433–456. Google Scholar | DOI

[2] [2] Cohn, P. M., On the free product of associative rings. III. J. Algebra 8 (1968, 376–383. Google Scholar | DOI

[3] [3] Dokuchaev, M. A. and Singer, M. L. S., Units in group rings of free products of prime cyclic groups. Canad. J. Math. 50 (1998, no. 2, 312–322. Google Scholar | DOI

[4] [4] Gerasimov, V. N., The group of units of a free product of rings. (Russian) Mat. Sb. 134(176)(1987), no. 1, 42–65; translation in Math. USSR-Sb. 62 (1989, no. 1, 41–63. Google Scholar

[5] [5] Ivanov, S. V., Strictly verbal products of groups and A. I. Mal’tsev's problem on operations over groups. (Russian) Trudy Moskov. Mat. Obshch. 54 (1992, 243–277, 279; translation in Trans. Moscow Math. Soc. 1993, 217–249. Google Scholar

[6] [6] Ivanov, S. V., The free Burnside groups of sufficiently large exponents. Internat. J. Algebra Comput. 4 (1994, no. 1–2, 1–308. Google Scholar

[7] [7] Ivanov, S. V., An asphericity conjecture and Kaplansky problem on zero divisors. J. Algebra 216 (1999, no. 1, 13–19. Google Scholar | DOI

[8] [8] Ivanov, S. V., On subgroups of free Burnside groups of large odd exponent. Illinois J. Math. 47 (2003, no. 1–2, 299–304. Google Scholar

[9] [9] Ivanov, S. V., Embedding free Burnside groups in finitely presented groups. Geom. Dedicata 111 (2005, 87–105. Google Scholar | DOI

[10] [10] Ivanov, S. V. The Kourovka Notebook: Unsolved problems in group theory. Eleventh ed., Russian Academy of Sciences Siberian Division, Institute of Mathematics, Novosibirsk, 1990. Google Scholar

[11] [11] Kurosh, A. G., The theory of groups. Chelsea, New York, 1956. Google Scholar

[12] [12] Ol’shanskii, A. Yu., On the Novikov-Adian theorem. (Russian) Mat. Sb. 118(160)(1982), no. 2, 203–235, 287. Google Scholar

[13] [13] Ol’shanskii, A. Yu., The geometry of defining relations in groups. Nauka, Moscow, 1989; English translation Math. and tts Applications, Soviet series, 70, Kluwer Acad. Publ., 1991. Google Scholar

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