SQ Universal Group
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the realm of group theory, a countable group is said to be SQ universal if every countable group can be embedded in one of its quotient groups. SQ-universality can be thought of as a measure of largeness or complexity of a group. Many classic results of combinatorial group theory, going back to 1949, are now interpreted as saying that a particular group or class of groups is (are) SQ-universal. However the first explicit use of the term seems to be ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the realm of group theory, a countable group is said to be SQ universal if every countable group can be embedded in one of its quotient groups. SQ-universality can be thought of as a measure of largeness or complexity of a group. Many classic results of combinatorial group theory, going back to 1949, are now interpreted as saying that a particular group or class of groups is (are) SQ-universal. However the first explicit use of the term seems to be in an address given by Peter Neumann to the The London Algebra Colloquium entitled "SQ-universal groups" on 23 May 1968. In 1949 Graham Higman, Bernhard Neumann and Hanna Neumann proved that every countable group can be embedded in a two generator group. Using the contemporary language of SQ-universality, this result says that F_2 , the free group (non-abelian) on two generators, is SQ-universal. This is the first known example of an SQ-universal group.
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