×

zbMATH — the first resource for mathematics

New criteria for the solvability of finite groups. (English) Zbl 0486.20018

MSC:
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D05 Finite simple groups and their classification
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arad, Z, Groups with S_{2}-subgroups and S3-subgroups, Israel J. math., 17, 76-83, (1974) · Zbl 0283.20011
[2] Brauer, R, Blocks of characters and structure of finite groups, Bull. amer. math. soc., 1, 21-38, (1979) · Zbl 0418.20006
[3] Carter, R.W, Simple groups of Lie type, (1972), Wiley London/New York/Sidney/Toronto · Zbl 0248.20015
[4] Feit, W; Thompson, J, Solvability of groups of odd order, Pacific J. math., 13, 775-1029, (1963) · Zbl 0124.26402
[5] Hall, P, A note on soluble groups, J. London math. soc., 3, 98-105, (1928) · JFM 54.0145.01
[6] Hall, P, A characteristic property of soluble groups, J. London math. soc., 12, 198-200, (1937) · Zbl 0016.39204
[7] Hall, P, Theorems like Sylow’s, (), 286-304 · Zbl 0075.23907
[8] Hartley, R.W, Determination of the ternary collineation groups whose coefficients Lie in GF(2n), Ann. of math., 27, 140-158, (1925) · JFM 51.0117.07
[9] Hunt, D.C, The character table of an eight-dimensional orthogonal group, Math. comp., 28, 659-660, (1974), (microfiche supplement) · Zbl 0278.20007
[10] Huppert, B, Endliche gruppen, I, (1967), Springer-Verlag Berlin/Heidelberg/New York · Zbl 0217.07201
[11] Janko, Z, A characterization of the simple group G2(3), J. algebra, 12, 360-371, (1969) · Zbl 0177.04001
[12] Parrot, D, A characterization of the Tits simple group, Canad. J. math., 24, 672-685, (1972) · Zbl 0241.20014
[13] Seitz, G.M, Flag transitive subgroups of Chevalley groups, Ann. of math., 97, 27-56, (1973) · Zbl 0338.20052
[14] Spitznagel, E.L, Hall subgroups of certain families of finite groups, Math. Z., 97, 259-290, (1967) · Zbl 0183.03104
[15] Suzuki, M, On a class of doubly transitive groups, Ann. of math., 75, 105-145, (1962) · Zbl 0106.24702
[16] Williams, J.S, Prime graph components of finite groups, J. algebra, 69, 487-513, (1981) · Zbl 0471.20013
[17] Zsigmondy, K, Zur theorie der potenzreste, Monatsh. math. phys., 3, 265-284, (1892) · JFM 24.0176.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.