Describing finite groups by short first-order sentences
نویسندگان
چکیده
منابع مشابه
Describing Finite Groups by Short First-order Sentences
We say that a class of finite structures for a finite signature is r-compressible if each structure G in the class has a first-order description of size at most O(r(|G|)). We show that the class of finite simple groups is log-compressible, and the class of all finite groups is log-compressible. The result relies on the classification of finite simple groups, the bi-interpretability of the small...
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For various proper inclusions of classes of groups C D, we nd a group H 2 D and a rst{order sentence ' such that H j = ' but no G 2 C sat-isses '. The classes we consider include the classes of nite, nitely presented, nitely generated with and without solvable word problem, and all countable groups. For one separation, we give an exampleof a f.g. group, namely ZpoZfor some prime p, which is the...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2017
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-017-1563-2