| Finite Groups with Character Degrees of Two Distinct Primes |
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| 作者姓名： | CHEN Shengan FAN Yun SHUM Karpin |
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| 作者单位： | [1]School of Mathematics trod Statistics, Wuhan University, Wuhan 430072, Hubei, China [2]Department of Mathematics, Xianning College, Xianning 437005, Hubei, China [3]Department of Mathematics, Chinese University of Hong Kong, Hong Kong, China |
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| 摘 要： | 0Introduction Characterdegreesoffinitegroupsandtheirsubgroupshavebeenrecentlystudied16].Inthisnote,westudytherelationshipsbetweenthegroup theoreticalstructureofafinitegroupGandthearithmeticpropertyofthedegreesofthe irreduciblecharactersofG.Afundamentalfactisthatifafi nitegroupGhasanabeliannormalsubgroupA,thenthede greeofanyirreduciblecharacterofGdividesthequotientorder|G/A|;seeTheorem6.15ofRef.2]andProperty24of Ref.7].ForfinitesolvablegroupsG,It gaveapartialin verse.Heshownthatifthede…
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| 关 键 词： | Abelian normal π-complement |
| 文章编号： | 1007-1202（2006）02-0343-03 |
| 收稿时间： | 2005-03-10 |
Finite groups with character degrees of two distinct primes |
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| CHEN Shengan FAN Yun SHUM Karpin.Finite Groups with Character Degrees of Two Distinct Primes[J].Wuhan University Journal of Natural Sciences,2006,11(2):343-345. |
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| Authors: | Chen Shengan Fan Yun Shum Karping |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, 430072 Wuhan, Hubei, China;(2) Department of Mathematics, Xianning College, 437005 Xianning, Hubei, China;(3) Department of Mathematics, Chinese University of Hong Kong, Hong Kong, China |
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| Abstract: | It is proved that if the degree of any non-linear irreducible character of a finite group G is a product of powers of two given distinct prime integers p and q, then G has an abelian Hall {p, q} subgroup H and an Abelian normal {p, q} complement A, and the centralizer in A of the Sylow p-subgroup of G is equal to the centralizer in A of the Sylow q-subgroup of G. |
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| Keywords: | degree of character centralizer semi-direct product |
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