A characterization of 𝑈₃(2ⁿ) by its Sylow 2-subgroup

Griess, Robert L.

doi:10.1090/S0002-9947-1973-0318292-4

A characterization of $U_{3}(2^{n})$ by its Sylow $2$-subgroup
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by Robert L. Griess

Trans. Amer. Math. Soc. 175 (1973), 181-186

DOI: https://doi.org/10.1090/S0002-9947-1973-0318292-4

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Abstract:

We determine all the finite groups having a Sylow 2-subgroup isomorphic to that of ${U_3}({2^n}),n \geq 3$. In particular, the only such simple groups are the ${U_3}({2^n})$.

References

Michael J. Collins, The characterisation of the unitary groups $\textrm {U}_{3}(2^{n})$ by their Sylow $2$-subgroups, Bull. London Math. Soc. 4 (1972), 49–53. MR 340441, DOI 10.1112/blms/4.1.49
Walter Feit and John G. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775–1029. MR 166261
Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
Daniel Gorenstein and John H. Walter, Centralizers of involutions in balanced groups, J. Algebra 20 (1972), 284–319. MR 292927, DOI 10.1016/0021-8693(72)90060-9

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Michio Suzuki, Finite groups in which the centralizer of any element of order $2$ is $2$-closed, Ann. of Math. (2) 82 (1965), 191–212. MR 183773, DOI 10.2307/1970569
John H. Walter, The characterization of finite groups with abelian Sylow $2$-subgroups, Ann. of Math. (2) 89 (1969), 405–514. MR 249504, DOI 10.2307/1970648