\(p\)-groups of automorphisms of Abelian \(p\)-groups. (English. Russian original) Zbl 0979.20051
Algebra Logika 39, No. 3, 359-371 (2000); translation in Algebra Logic 39, No. 3, 207-214 (2000).
Let \(G\) be a \(p\)-group contained in the automorphism group of an Abelian \(p\)-group \(A\). The author studies connections between \(C_G(\Omega_1(A))\) and \(C_G(A/pA)\). It is proved that the exponent of \(C_G(\Omega_1(A))\) is finite if and only if so is the exponent of \(C_G(A/pA)\).
Reviewer: E.P.Vdovin (Novosibirsk)
MSC:
| 20K30 | Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups |
| 20K10 | Torsion groups, primary groups and generalized primary groups |
| 20F50 | Periodic groups; locally finite groups |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20D45 | Automorphisms of abstract finite groups |
| 20F28 | Automorphism groups of groups |
