Recognizing the prime divisors of the index of a proper subgroup. (Q657991)
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scientific article; zbMATH DE number 5996446
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Recognizing the prime divisors of the index of a proper subgroup. |
scientific article; zbMATH DE number 5996446 |
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Recognizing the prime divisors of the index of a proper subgroup. (English)
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11 January 2012
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Let \(C\) be a subgroup of a finite group \(G\). It is proved, inter alia, that the set of primes dividing \(|G:C|\) is contained in the set of primes dividing \(|H:C\cap H|\) for some 3-generator subgroup \(H\). There are also several other more general results of similar nature. The authors conjecture that ``3-generator'' could be replaced by ``2-generator'', and produce two partial results in support of this conjecture.
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prime divisors
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subgroup indices
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finite groups
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3-generator subgroups
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