On the solvability of commutative loops and their multiplication groups (Q2761018)
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scientific article; zbMATH DE number 1682882
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solvability of commutative loops and their multiplication groups |
scientific article; zbMATH DE number 1682882 |
Statements
17 December 2001
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solvability of finite groups
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solvability of finite loops
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finite commutative loops
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inner mapping groups
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On the solvability of commutative loops and their multiplication groups (English)
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The main result of the paper asserts that if a group \(G\) contains a subgroup of order \(2p\), where \(p=4t+3\) is a prime, then \(G\) is solvable (Thm. 2.1). From this it follows that if \(Q\) is a finite commutative loop such that the inner mapping group \(I(Q)\) is of order \(2p\), with \(p\) as above, then \(Q\) is a solvable loop (Thm. 2.3).
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