Properties of Infinite Groups
For an infinite group, a "small neighborhood" is taken to be a finitely generated subgroup. An infinite group is said to be locally P if every finitely generated subgroup is P. For instance, a group is locally finite if every finitely generated subgroup is finite. A group is locally soluble if every finitely generated subgroup is soluble.
Read more about this topic: Local Property
Famous quotes containing the words properties of, properties, infinite and/or groups:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“Idleness [is] only a coarse name for my infinite capacity for living in the present.”
—Cyril Connolly (1903–1974)
“... until both employers’ and workers’ groups assume responsibility for chastising their own recalcitrant children, they can vainly bay the moon about “ignorant” and “unfair” public criticism. Moreover, their failure to impose voluntarily upon their own groups codes of decency and honor will result in more and more necessity for government control.”
—Mary Barnett Gilson (1877–?)