- If n ≥ 3, the group SLn(Z) is boundedly generated by its elementary subgroups, formed by matrices differing from the identity matrix only in one off-diagonal entry. In 1984, Carter and Keller gave an elementary proof of this result, motivated by a question in algebraic K-theory.
- A free group on at least two generators is not boundedly generated (see below).
- The group SL2(Z) is not boundedly generated, since it contains a free subgroup with two generators of index 12.
- A Gromov-hyperbolic group is boundedly generated if and only if it is virtually cyclic (or elementary), i.e. contains a cyclic subgroup of finite index.
Read more about this topic: Boundedly Generated Group
Other articles related to "examples":
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... though /oʊ/ as in toe (other examples dough) tough /ʌf/ as in cuff (other examples rough, enough) cough /ɒf/ as in off (other examples Gough (name, some pronunciations)) hiccough (a now uncommon ...
Famous quotes containing the word examples:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (16701733)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (18961966)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold peoples attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)