Pairs of matrices of order two which generate free groups
نویسندگان
چکیده
منابع مشابه
Pairs of matrices, one of which commutes with their commutator
Let A, B be n × n complex matrices such that C = AB − BA and A commute. For n = 2, we prove that A, B are simultaneously triangularizable. For n ≥ 3, we give an example of matrices A, B such that the pair (A, B) does not have property L of Motzkin-Taussky, and such that B and C are not simultaneously triangularizable. Finally, we estimate the complexity of the Alp’in-Koreshkov’s algorithm that ...
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Let [Formula: see text] be a finitely generated group, [Formula: see text] a finite set of generators and [Formula: see text] a subgroup of [Formula: see text]. We define what it means for [Formula: see text] to be a context-free pair; when [Formula: see text] is trivial, this specializes to the standard definition of [Formula: see text] to be a context-free group. We derive some basic properti...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1957
ISSN: 0019-2082
DOI: 10.1215/ijm/1255380395