of group theory, a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups. Characteristically simple groups...

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...

abelian group is a fully invariant subgroup. The identity component of a topological group is always a characteristic subgroup. Characteristically simple group...

mathematics, the classification of finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or...

of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic...

classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one...

classification of finite simple groups says that most finite simple groups arise as the group G(k) of k-rational points of a simple algebraic group G over a finite...

disconnected groups were obtained in 2011 by Caprace and Monod, with notably a classification of characteristically simple groups and of Noetherian groups. In...

known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having...

finite simple groups of Lie type does have a precise definition, and they make up most of the groups in the classification of finite simple groups. The...

the parent group. characteristically simple group A group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups...

over a field of characteristic 2. In the classification of finite simple groups, there is a major division between group of characteristic 2 type, where...

mathematics, a quasithin group is a finite simple group that resembles a group of Lie type of rank at most 2 over a field of characteristic 2. The classification...

social group or between social groups is known as group dynamics. A social group exhibits some degree of social cohesion and is more than a simple collection...

classification of finite simple groups, especially for simple groups whose characterization was not amenable to purely group-theoretic methods because...

In the mathematical classification of finite simple groups, a thin group is a finite group such that for every odd prime number p, the Sylow p-subgroups...

finite group is a direct sum of simple representations (provided the characteristic of the base field does not divide the order of the group). So in...

mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any non-zero...

(Note that not every simple algebra is a central simple algebra over its center: for instance, if K is a field of characteristic 0, then the Weyl algebra...

A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the performance of a binary classifier model (can be used...

rotation group, SO(3, R) SO(8) indefinite orthogonal group unitary group symplectic group list of finite simple groups list of simple Lie groups Representations...

it a simple metre. More specifically, it is a simple triple metre because there are three beats in each measure; simple duple (two beats) or simple quadruple...

Simplicity is the state or quality of being simple. Something easy to understand or explain seems simple, in contrast to something complicated. Alternatively...

above. In this setting, the Euler characteristic of a finite group or monoid G is 1/ | G | , and the Euler characteristic of a finite groupoid is the sum...

has only simple zeros. The latter condition is always satisfied if E has characteristic 0. For a finite Galois extension, the Galois group Gal(F/E) is...

The center of a nonabelian simple group is trivial. The center of the dihedral group, Dn, is trivial for odd n ≥ 3. For even n ≥ 4...

algebraic group over R (necessarily R-anisotropic and reductive), as can many noncompact groups such as the simple Lie group SL(n,R).) The simple Lie groups were...

generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. An abelian group is a...

and patterns that rise and fall are called chants. Songs composed in a simple style that are learned informally "by ear" are often referred to as folk...

generalizing the Suzuki groups found by Suzuki using a different method. They were the last of the infinite families of finite simple groups to be discovered...