Obstruction to a Higman embedding theorem for residually finite groups with solvable word problem

Rauzy Emmanuel

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Obstruction to a Higman embedding theorem for residually finite groups with solvable word problem

机译：用可解词问题妨碍剩余有限组嵌入定理的人

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We prove that, for a finitely generated residually finite group, having solvable word problem is not a sufficient condition to be a subgroup of a finitely presented residually finite group. The obstruction is given by a residually finite group with solvable word problem for which there is no effective method that allows, given some non-identity element, to find a morphism onto a finite group in which this element has a non-trivial image. We also prove that the depth function of this group grows faster than any recursive function.

机译：我们证明了，对于有限生成的剩余有限群，有可解字问题不是成为有限呈现剩余有限群子群的充分条件。障碍是由一个具有可解字问题的剩余有限群给出的，对于这个问题，没有有效的方法允许在给定一些非同一元素的情况下，找到有限群上的态射，其中该元素有一个非平凡的映像。我们还证明了这个群的深度函数的增长速度比任何递归函数都快。

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《Journal of group theory》 |2021年第3期|共8页
作者
Rauzy Emmanuel;
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Univ Paris Inst Math Jussieu Paris Rive Gauche UFR Math Batiment Sophie Germain 8 Pl Aurelie Nemours F-75013 Paris France;

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Obstruction to a Higman embedding theorem for residually finite groups with solvable word problem

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