Théorie des groupes
Finite groups with Quaternion Sylow subgroup
Comptes Rendus. Mathématique, Tome 358 (2020) no. 9-10, pp. 1097-1099.

In this paper we show that a finite group G with Quaternion Sylow 2-subgroup is 2-nilpotent if, either 3|G| or G is solvable and the order of its Sylow 2-subgroup is strictly greater than 16.

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DOI : 10.5802/crmath.131
Classification : 20D99, 20E45
Mousavi, Hamid 1

1 Department of Mathematical Sciences, University of Tabriz, P.O.Box 51666-16471, Tabriz, Iran
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Mousavi, Hamid. Finite groups with Quaternion Sylow subgroup. Comptes Rendus. Mathématique, Tome 358 (2020) no. 9-10, pp. 1097-1099. doi : 10.5802/crmath.131. http://www.numdam.org/articles/10.5802/crmath.131/

[1] Brauer, Richard; Suzuki, Michio On finite groups of even order whose 2-Sylow group is a Quaternion group, Proc. Natl. Acad. Sci. USA, Volume 45 (1959), pp. 1757-1759 | DOI | MR | Zbl

[2] Collins, Michael J. The characterisation of the Suzuki groups by their Sylow 2-subgroups, Math. Z., Volume 123 (1971), pp. 32-48 | DOI | MR | Zbl

[3] The GAP Group GAP – Groups, Algorithms, and Programming, Version 4.11.0, 2020 (http://www.gap-system.org)

[4] Glauberman, George Factorizations in local subgroups of finite groups, Regional Conference Series in Mathematics, 33, American Mathematical Society, 1977 | MR | Zbl

[5] Gorenstein, Daniel; Walter, John H. The characterization of finite groups with dihedral Sylow 2-subgroups I., II., III, J. Algebra, Volume 2 (1965), p. 85-151; 218–270; 334–393 | DOI | Zbl

[6] Isaacs, I. Martin Finite group theory, Graduate Studies in Mathematics, 92, American Mathematical Society, 2008 | MR | Zbl

[7] Kohl, Stefan Counting the orbits on finite simple groups under the action of the automorphism group – Suzuki groups vs. linear groups, Commun. Algebra, Volume 30 (2002) no. 7, pp. 3515-3532 | DOI | MR | Zbl

[8] Wong, Warren J. On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2, J. Aust. Math. Soc., Volume 4 (1964), pp. 90-112 | DOI | MR | Zbl

[9] Wong, Warren J. On Finite Groups with Semi-Dihedral Sylow 2-Subgroups, J. Algebra, Volume 4 (1966), pp. 52-63 | DOI | MR

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