Fixed points of \(p\)-automorphisms of finite \(p\)-groups. (English. Russian original) Zbl 0407.20019
Algebra Logic 14(1975), 417-420 (1976); translation from Algebra Logika 14, 697-703 (1975).
MSC:
| 20D45 | Automorphisms of abstract finite groups |
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
| 20D30 | Series and lattices of subgroups |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
| 20D25 | Special subgroups (Frattini, Fitting, etc.) |
Keywords:
Sylow \(p\)-subgroups of class at most \(p-1\); \(p\)-automorphisms; Hall \(p'\)-subgroups; finite \(p\)-groupsCitations:
Zbl 0132.016References:
| [1] | J. Thompson, ”Fixed points ofP-groups acting onP-groups,” Math. Z.,86, 12, 13 (1964). · Zbl 0132.01601 · doi:10.1007/BF01111272 |
| [2] | M. Hall, The Theory of Groups, Macmillan, New York (1959). · Zbl 0084.02202 |
| [3] | D. Gorenstein, Finite Groups, Harper and Row (1968). · Zbl 0185.05701 |
| [4] | L. Evens, ”On a theorem of Thompson on fixed points of groups acting onP-groups,” Math. Z.,93, No. 2, 105–108 (1966). · Zbl 0144.01601 · doi:10.1007/BF01111029 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
