On finite simple groups with a self-centralization system of type (2(𝑛))

Ferguson, Pamela A.

doi:10.1090/S0002-9939-1978-0509231-1

On finite simple groups with a self-centralization system of type $(2(n))$
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by Pamela A. Ferguson

Proc. Amer. Math. Soc. 72 (1978), 443-444

DOI: https://doi.org/10.1090/S0002-9939-1978-0509231-1

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Abstract:

Let G denote a simple group with a self-centralization system of type $(2(n))$, where $n > 3$. Let ${X_1}$ denote an exceptional character of G, then ${X_1}(1) = kn + 2\varepsilon$ where $\varepsilon = \pm 1$. It is known that \[ |G| = nX_{1}(1)(X_{1}(1)-\varepsilon )(ln + 1) \] where l is a nonnegative integer. In this paper G is classified if $l = 0,\varepsilon = 1$ and ${X_1}(1)$ is odd.

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