关于群的自由积的商群与导群

On Quotient Group and Derived Group of Free Product of Groups

设A,B是群,其自由积的商群(A*B)/NA B,其中NA为A生成的正规子群.A*B的导群中一般元素形如w=a1b1…akbk,适当排列元素次序后,a1,…,ak之积为eA,b1,…,bk之积为eB.文中还讨论了某些特殊情形.

Let A and B be groups, and the quotient group of their free product is （ A ＊ B ）/NA ≌ B, where NA is the normal subgroup generated by A. Any element of derived subgroup of A ＊ B is the form, w = a1 b1…akbk, where the product of a1,…, ak is eA and the product of b1 ,…, bk is eB after properly arranging the orders of dements. Some special cases are also considered in the paper.