Geodesic
On Unsolvable Groups of Degree p = 4q + 1, p and q Primes
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 583-589

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This paper presents two results. They are:Theorem 1. Let G be a doubly transitive permutation group of degree nq + 1 where a is a prime and n < g. If G is neither alternating nor symmetric, then G has Sylow q-subgroup of order only q.Result 2. There is no unsolvable transitive permutation group of degree p = 29, 53, 149, 173, 269, 293, or 317 properly contained in the alternating group of degree p.Result 2 was demonstrated by a computation on the Illiac II computer at the University of Illinois. 
Appel, K. I.; Parker, E. T. On Unsolvable Groups of Degree p = 4q + 1, p and q Primes. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 583-589. doi: 10.4153/CJM-1967-051-2
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[1] 1. Burnside, W., Theory of groups of finite order, 2nd ed. (Cambridge, 1911). Google Scholar

[2] 2. Hall, M. Jr., The theory of groups (New York, 1959). Google Scholar

[3] 3. Ito, N., Zur Theorie der Permutationsgruppen von Grad p, Math. Z., 74 (1960), 299–301. Google Scholar

[4] 4. Miller, G. A., Limits of the degree of transitivity of substitution groups, Bull. Amer. Math Soc., 22 (1915), 68–71. Google Scholar

[5] 5. Parker, E. T., On quadruply transitive groups, Pacific J. Math., 9 (1959), 829–836. Google Scholar

[6] 6. Parker, E. T. and Nikolai, J., A search for analogues of the Mathieu groups, Math Comput., 12 (1958), 38–43. Google Scholar

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