In this paper we show that a finite group with Quaternion Sylow -subgroup is -nilpotent if, either or is solvable and the order of its Sylow -subgroup is strictly greater than .
Revised:
Accepted:
Published online:
Hamid Mousavi 1
@article{CRMATH_2020__358_9-10_1097_0, author = {Hamid Mousavi}, title = {Finite groups with {Quaternion} {Sylow} subgroup}, journal = {Comptes Rendus. Math\'ematique}, pages = {1097--1099}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {9-10}, year = {2020}, doi = {10.5802/crmath.131}, language = {en}, }
Hamid Mousavi. Finite groups with Quaternion Sylow subgroup. Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1097-1099. doi : 10.5802/crmath.131. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.131/
[1] On finite groups of even order whose -Sylow group is a Quaternion group, Proc. Natl. Acad. Sci. USA, Volume 45 (1959), pp. 1757-1759 | DOI | MR | Zbl
[2] The characterisation of the Suzuki groups by their Sylow -subgroups, Math. Z., Volume 123 (1971), pp. 32-48 | DOI | MR | Zbl
[3] GAP – Groups, Algorithms, and Programming, Version 4.11.0, 2020 (http://www.gap-system.org)
[4] Factorizations in local subgroups of finite groups, Regional Conference Series in Mathematics, 33, American Mathematical Society, 1977 | MR | Zbl
[5] The characterization of finite groups with dihedral Sylow -subgroups I., II., III, J. Algebra, Volume 2 (1965), p. 85-151; 218–270; 334–393 | DOI | Zbl
[6] Finite group theory, Graduate Studies in Mathematics, 92, American Mathematical Society, 2008 | MR | Zbl
[7] 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] 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] On Finite Groups with Semi-Dihedral Sylow -Subgroups, J. Algebra, Volume 4 (1966), pp. 52-63 | DOI | MR
Cited by Sources:
Comments - Politique