We call a finite group irrational if none of its elements is conjugate to adistinct power of itself. We prove that those groups are solvable and describecertain classes of these groups, where the above property is only required for$p$-elements, for $p$ from a prescribed set of primes.
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机译:如果一个有限群的元素都不与它自身的独特力量共轭,我们称其为非理性有限群。我们证明了这些组是可解的,并描述了这些组中的某些类别,其中,仅对于$ p $元素(从规定的素数集中)需要上述属性。
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