In this paper we study the \(\kappa \)-word problem for the pseudovariety \(\mathbf{LG}\) of local groups, where \(\kappa \) is the canonical signature consisting of the multiplication and the pseudoinversion. We solve this problem by transforming each arbitrary \(\kappa \)-term \(\alpha \) into another one \(\alpha ^*\) called the \(\mathbf{LG}\)-canonical form of \(\alpha \) and by showing that different canonical forms have different interpretations over \(\mathbf{LG}\). The procedure of construction of these canonical forms consists in applying reductions determined by a set \(\Sigma \) of \(\kappa \)-identities. As a consequence, \(\Sigma \) is a basis of \(\kappa \)-identities for the \(\kappa \)-variety generated by \(\mathbf{LG}\).

在本文中，我们研究了\（\卡帕\） -word为pseudovariety问题\（\ mathbf {LG} \）的本地组，其中\（\卡帕\）是由乘法和pseudoinversion的规范签名。我们通过将每个任意的\(\kappa \) -term \(\alpha \)转换为另一个\(\alpha ^*\) 来解决这个问题，称为\(\mathbf{LG}\) -规范形式的\( \alpha \)并通过证明不同的规范形式对\(\mathbf{LG}\)有不同的解释。构建这些规范形式的过程包括应用由集合\(\Sigma \)的\（\卡帕\） -identities。因此，\(\Sigma \)是由\(\mathbf{LG}\)生成的\(\kappa \) -variety的\(\kappa \) -identities的基础。