Abstract
The purpose of this paper is to show that the exceptional possibilities in the main theorem of [3] do not occur. This then strengthens that theorem.
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Gorenstein, D., Lyons, R., Solomon, R.: The Classification of the Finite Simple Groups. Number 3. Part I. Chapter A. Almost Simple \(K\)-groups. Mathematical Surveys and Monographs, 40.3. American Mathematical Society, Providence, RI (1998)
Kondratev, A.S.: Finite linear groups of degree six. Algebra and Logic 28(1989), 122–138 (1990)
Mainardis, M., Meierfrankenfeld, U., Parmeggiani, G., Stellmacher, B.: The \({\tilde{P}}!\)-theorem. J. Algebra 292, 363–392 (2005)
Meierfrankenfeld, U., Stellmacher, B., Stroth, G.: The local structure theorem for finite groups with a large \(p\)-subgroup. Mem. Amer. Math. Soc. 242(1147), vii + 342 pp. (2016)
Parker, C., Parmeggiani, G., Stellmacher, B.: The \(P!\)-theorem., J. Algebra 263, 17–58 (2003)
Parker, C., Reza Salarian, M., Stroth, G.: A characterisation of almost simple groups with socle \({}^2{{\rm E}}_6(2)\) or \({{\rm M}}(22)\). Forum Math. 27, 2853–2901 (2015)
Parker, C., Wiedorn, C.: A \(5\)-local identification of the monster. Arch. Math. (Basel) 83, 404–415 (2004)
Winter, D.: The automorphism group of an extraspecial \(p\)-group. Rocky Mountain J. Math. 2, 159–168 (1972)
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Parker, C., Stroth, G. On the \(\tilde{P}!\)-theorem. Arch. Math. 118, 123–132 (2022). https://doi.org/10.1007/s00013-021-01675-0
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DOI: https://doi.org/10.1007/s00013-021-01675-0