Coprimeness among irreducible character degrees of finite solvable groups
Coprimeness among irreducible character degrees of finite solvable groups
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DOI：
10.1090/s0002-9939-97-04269-x
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发表时间：
1997
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影响因子：
--
通讯作者：
D. Benjamin
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文献类型：
--
作者：
D. Benjamin
.给定一个有限可解群G，我们说G具有性质Pk，如果G的每个k个不同的不可约特征标度的集合是（按集）互素的。设k（G）是使G萨蒂斯性质Pk的最小正整数.我们得到了G的不可约特征标度总数在k（G）中是二次的一个界。三个例外的情况下发生，构造的例子，验证在这些特殊情况下的界限的清晰度。
. Given a finite solvable group G , we say that G has property P k if every set of k distinct irreducible character degrees of G is (setwise) relatively prime. Let k ( G ) be the smallest positive integer such that G satisfies property P k . We derive a bound, which is quadratic in k ( G ), for the total number of irreducible character degrees of G . Three exceptional cases occur; examples are constructed which verify the sharpness of the bound in each of these special cases.