Two subgroups A and B of a group G are said to be 𝒩{\mathcal{N}}-connected if, for all a in A and b in B , the subgroup generated by a and b is a nilpotent group. In this paper, we study the structure of a group G assuming that G=A⁢B{G=AB} and A and B are 𝒩{\mathcal{N}}-connected subgroups satisfying Max or Min.

中文翻译：

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群产品中的幂等关系

如果对于A中的所有a和B中的b而言，由a和b生成的子组是幂等组，则将组G的两个子组A和B称为𝒩{\ mathcal {N}}连接。在本文中，我们假设G =A⁢B{G = AB}且A和B是满足Max或Min的𝒩{\ mathcal {N}}连接子组，我们研究G组的结构。