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\(p\)-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 \(C_G(A/pA)\).
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
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