We consider word automaticity for groups that are nilpotent of class 2 and have exponent a prime p. We show that the infinitely generated free group in this variety is not word automatic. In contrast, the infinite extra-special p-group $E_p$ is word automatic, as well as an intermediate group $H_p$ which has an infinite centre. In the last section we introduce a method for showing automaticity of central extensions of abelian groups via co-cycles.

中文翻译：

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2 级幂零词自动群

我们考虑 2 类幂零且指数为素数p的群的词自动性。我们表明，该变体中无限生成的自由群不是单词自动的。相反，无限特特殊p群${乙}_p$是单词自动的，也是中间组$H_p$它有一个无限的中心。在上一节中，我们介绍了一种通过共循环来显示交换群中心扩展的自动性的方法。