\(p\)-groups of automorphisms of Abelian \(p\)-groups (Q2746916)
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scientific article; zbMATH DE number 1656854
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(p\)-groups of automorphisms of Abelian \(p\)-groups |
scientific article; zbMATH DE number 1656854 |
Statements
11 October 2001
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automorphism groups
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Abelian \(p\)-groups
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groups of finite exponent
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\(p\)-groups of automorphisms
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\(p\)-groups of automorphisms of Abelian \(p\)-groups (English)
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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 \(C_G(A/pA)\).
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