Abstract A group G is called mixed identity-free if for every and every there exists a homomorphism such that is the identity on G and is nontrivial. In this paper, we make a modification to the construction of elementary amenable lacunary hyperbolic groups provided by Ol’shanskii et al. to produce finitely generated elementary amenable groups which are mixed identity-free. As a byproduct of this construction, we also obtain locally finite p-groups which are mixed identity-free.

中文翻译：

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混合无身份基本服从群体

摘要 如果群 G 中的每一个都存在一个同态，它是 G 上的恒等且是非平凡的，那么群 G 被称为混合无恒等。在本文中，我们对 Ol'shanskii 等人提供的基本适用的空缺双曲群的构造进行了修改。产生有限生成的基本服从群，这些群是混合无身份的。作为这种构造的副产品，我们还获得了混合无身份的局部有限 p 群。