free group

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free group

[′frē ‚grüp]
(mathematics)
A group whose generators satisfy the equation x · y = e (e is the identity element in the group) only when x = y -1 or y = x -1.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Nickolas, "A free subgroup of the free abelian topological group on the unit interval," Bulletin of the London Mathematical Society, vol.
From a result of Baumslag [1], if G and H are finite groups, then the amalgamated free product [G.sub.*A] H contains a free subgroup of finite index.
The free product Z/pZ * Z/qZ has a finite index free subgroup F over which the central extension splits.
The authors cover hyperbolic spaces and group actions, relative presentations and isoperimetric functions, isolated components in geodesic polygons, rotating families and windmills, hyperbolic cone-off, WPD elements and elementary subgroups, hyperbolically embedded virtually free subgroups, rotating families from small cancellation subgroups, Dhen filling, diagram surgery, largeness properties, and a wide variety of other related subjects and topic areas.
Kramer, Multiplicity free subgroups of compact connected Lie groups, Arch.