In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, a normal subgroup and the quotient group, and the process can be repeated. If the group is finite, then eventually one arrives at uniquely determined simple groups by the Jordan–Hölder theorem.
Read more about Simple Group: Structure of Finite Simple Groups, History For Finite Simple Groups, Tests For Nonsimplicity
Famous quotes containing the words simple and/or group:
“The prostitute is the scapegoat for everyone’s sins, and few people care whether she is justly treated or not. Good people have spent thousands of pounds in efforts to reform her, poets have written about her, essayists and orators have made her the subject of some of their most striking rhetoric; perhaps no class of people has been so much abused, and alternatively sentimentalized over as prostitutes have been but one thing they have never yet had, and that is simple legal justice.”
—Alison Neilans. “Justice for the Prostitute—Lady Astor’s Bill,” Equal Rights (September 19, 1925)
“Just as a person who is always asserting that he is too good-natured is the very one from whom to expect, on some occasion, the coldest and most unconcerned cruelty, so when any group sees itself as the bearer of civilization this very belief will betray it into behaving barbarously at the first opportunity.”
—Simone Weil (1910–1943)