We prove a conjecture of J. Carlson, N. Mazza and J. Th\'evenaz; namely, wewill prove that if $G$ is a finite $p$-nilpotent group which contains anon-cyclic elementary Abelian $p$-subgroup and $k$ is an algebraically closedfield of characteristic $p$, then all simple endo-trivial $kG$-modules are$1$-dimensional.
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机译：我们证明了J. Carlson，N。Mazza和J. Th \'evenaz的猜想；就是说，我们将证明，如果$ G $是一个有限的$ p $-无能组，其中包含一个非循环基本Abelian $ p $-子组，而$ k $是一个具有特征性$ p $的代数闭域，则所有简单的内平凡的$ kG $-模块是$ 1 $维。
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