In most cases ( and } } ), is a perfect group and is a finite simple group,.
12.
Holt and Plesken's Perfect Groups classification is missing two groups, and Sims's Primitive Groups classification switched two groups.
13.
For a finite group, the derived series terminates in a perfect group, which may or may not be trivial.
14.
A non-trivial finite perfect group which is not simple must then be an extension of at least one smaller simple non-abelian group.
15.
From that stronger theorem Remak also proved various corollaries including that groups with a trivial center and perfect groups have a unique Remak decomposition.
16.
Rosenow figures his nonprofit foundation, whose million members nationwide are dedicated to preserving trees, is a perfect group to help advance those goals in the golf world.
17.
The Schur cover of a perfect group is uniquely determined up to isomorphism, but the Schur cover of a general finite group is only determined up to isoclinism.
18.
A non-trivial perfect group, however, is necessarily not solvable; and 4 divides its order ( if finite ), moreover, if 8 does not divide the order, then 3 does.
19.
With every perfect group " G " one can associate a ( canonical, terminal ) acyclic space, whose fundamental group is a central extension of the given group " G ".
20.
A finite perfect group is superperfect if and only if it is its own universal central extension ( UCE ), as the second homology group of a perfect group parametrizes central extensions.
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