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Abstract
Let H be a finite group, and let θ be an automorphism of H whose order divides n. Hall proved that the number of elements x of H that satisfy the relation x*xθ*xθ2 ***xθn-1 = 1 is a multiple of gcd(n,|H|). For a prime factor p of gcd(n,|H|), if such a number is not a multiple of gcd(pn,|H|), then a Sylow p-subgroup of H is exceptional.
Journal
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- Journal of Algebra
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Journal of Algebra 271 (1), 312-326, 2004-01-01
Elsevier
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Details 詳細情報について
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- CRID
- 1050282677542272640
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- NII Article ID
- 120006630166
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- NII Book ID
- AA11541904
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- HANDLE
- 10258/00009880
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- ISSN
- 00218693
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB
- CiNii Articles
- KAKEN