We prove analogues of Malyshev’s theorems on the structure of finite ##IMG## [http://ej.iop.org/images/1064-5616/211/2/291/toc_MSB_211_2_291ieqn1.gif] {$n$} -quasigroups with the weak invertibility condition and of Belousov’s theorem with a description of ##IMG## [http://ej.iop.org/images/1064-5616/211/2/291/MSB_211_2_291ieqn2.gif] {$(i,j)$} -associative ##IMG## [http://ej.iop.org/images/1064-5616/211/2/291/toc_MSB_211_2_291ieqn1.gif] {$n$} -quasigroups for the case of strongly dependent ##IMG## [http://ej.iop.org/images/1064-5616/211/2/291/toc_MSB_211_2_291ieqn1.gif] {$n$} -ary semigroup operations on a finite set. Bibliography: 8 titles.

中文翻译：

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部分可逆的高度相关的## IMG ## [http://ej.iop.org/images/1064-5616/211/2/291/toc_MSB_211_2_291ieqn1.gif] {$ n $} -ary操作

我们证明了有限## IMG ##结构上的Malyshev定理的类似物[http://ej.iop.org/images/1064-5616/211/2/291/toc_MSB_211_2_291ieqn1.gif] {$ n $}-拟群具有弱可逆性条件和Belousov定理，并带有## IMG ##的描述[http://ej.iop.org/images/1064-5616/211/2/291/MSB_211_2_291ieqn2.gif] {$（i， j）$} -associative ## IMG ## [http://ej.iop.org/images/1064-5616/211/2/291/toc_MSB_211_2_291ieqn1.gif] {$ n $}-对于强依赖## IMG ## [http://ej.iop.org/images/1064-5616/211/2/291/toc_MSB_211_2_291ieqn1.gif] {$ n $}-有限集上的半半组运算。参考书目：8种。