Let $G$ be a finite group and $chi$ be an irreducible character of $G$. An efficientand simple method to construct representations of finite groups is applicablewhenever $G$ has a subgroup $H$ such that $chi_H$has a linear constituent with multiplicity $1$.In this paper we show (with a few exceptions) that if $G$is a simple group or a covering group of a simple group and$chi$ is an irreducible character of $G$ of degree less than 32,then there exists a subgroup $H$ (often a Sylow subgroup) of $G$such that $chi_H$ has a linear constituent with multiplicity $1$.
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机译：假设$ G $为有限群，而$ chi $为$ G $的不可约性。只要$ G $有一个子组$ H $使得$ chi_H $具有一个具有多重性$ 1 $的线性成分，就可以使用一种有效且简单的方法来构造有限群的表示。在本文中，我们证明（除少数例外） $是一个简单组或一个简单组的覆盖组，而$ chi $是$ G $的度数小于32的不可约性，则存在$ G $的子组$ H $（通常是Sylow子组） $ chi_H $的线性成分的乘积为$ 1 $。
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