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...

classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either cyclic...

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...

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

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; it has...

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...

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...

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...

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...

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

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...

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

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...

Then M/Z(H) is a product of simple or cyclic groups as it is characteristically simple. If M/Z(H) is a product of cyclic groups then M must be in the Fitting...

area of modern algebra known as group theory, the Janko group J2 or the Hall-Janko group HJ is a sporadic simple group of order    604,800 = 27 · 33 ·...

A Simple Plan is a 1998 neo-noir crime thriller film directed by Sam Raimi and written by Scott B. Smith, based on Smith's 1993 novel. The film stars Bill...

abelian group is a direct product of cyclic groups. Every cyclic group of prime order is a simple group, which cannot be broken down into smaller groups. In...

arranged in a singular layer of cells as simple epithelium, either simple squamous, simple columnar, or simple cuboidal, or in layers of two or more cells...

(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...

and 2004, that culminated in a complete classification of finite simple groups. Group theory has three main historical sources: number theory, the theory...

In mathematics, G2 is three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras g 2 , {\displaystyle {\mathfrak...

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...

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...

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...

only finite groups will be considered in this article. We will also restrict ourselves to vector spaces over fields of characteristic zero. Because...

the permutations of X. The group operation in a symmetric group is function composition, denoted by the symbol ∘ or by simple juxtaposition. The composition...

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