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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 $$C_G(A/pA)$$.
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
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