标题： 关于不变有限$L$-表示的群的一点说明 显示英文标题

标题： A Note on Invariantly Finitely $L$-Presented Groups

摘要： 在本文的第一部分中，我们引入了$L$-表示的Tietze变换。 这些变换使我们能够将Tietze定理从有限表示群推广到不变有限$L$-表示群。 此外，它们允许我们证明“不变有限$L$-表示”是群的一个抽象性质，该性质不依赖于生成集。 在本文的第二部分中，我们考虑有限表示群的有限生成正规子群。 Benli证明了当商群为无限循环时，有限表示群的有限生成正规子群是不变有限$L$-表示的。 我们将这一结果推广到有限表示群在其有限生成子群上可分解的情况，以及商群为挠自由秩至多为二的交换群的情况。 显示英文摘要

摘要： In the first part of this note, we introduce Tietze transformations for $L$-presentations. These transformations enable us to generalize Tietze's theorem for finitely presented groups to invariantly finitely $L$-presented groups. Moreover, they allow us to prove that `being invariantly finitely $L$-presented' is an abstract property of a group which does not depend on the generating set. In the second part of this note, we consider finitely generated normal subgroups of finitely presented groups. Benli proved that a finitely generated normal subgroup of a finitely presented group is invariantly finitely $L$-presented whenever its quotient is infinite cyclic. We generalize this result to the case where the finitely presented group splits over its finitely generated subgroup and to the case where the quotient is abelian with torsion-free rank at most two.