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...

a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple Lie groups can...

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...

SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are...

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

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...

a group is said to be almost simple if it contains a non-abelian simple group and is contained within the automorphism group of that simple group – that...

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...

quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed...

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...

mathematics, a quasisimple group (also known as a covering group) is a group that is a perfect central extension E of a simple group S. In other words, there...

List of simple groups may refer to: List of finite simple groups List of simple Lie groups This disambiguation page lists articles associated with the...

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...

simple groups are sometimes also termed elementary groups. Characteristically simple is a weaker condition than being a simple group, as simple groups must...

Simple Minds are a Scottish rock band formed in Glasgow in 1977, becoming best known internationally for their song "Don't You (Forget About Me)" (1985)...

simple groups of Lie type, 63 and 36 are both exponents that figure in the orders of three exceptional groups of Lie type. The orders of these groups...

complete classification of finite simple groups was achieved, meaning that all those simple groups from which all finite groups can be built are now known....

In group theory, the Tits group 2F4(2)′, named for Jacques Tits (French: [tits]), is a finite simple group of order    17,971,200 = 211 · 33 · 52 · 13...

Look up simple in Wiktionary, the free dictionary. Simple or SIMPLE may refer to: Simplicity, the state or quality of being simple Simple (album), by...

In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups M11, M12, M22, M23 and M24 introduced by Mathieu (1861...

In mathematics, in the field of group theory, a group is said to be absolutely simple if it has no proper nontrivial serial subgroups. That is, G {\displaystyle...

group of its fundamental group. For the outer automorphism groups of all finite simple groups see the list of finite simple groups. Sporadic simple groups...

In mathematics, in the field of group theory, a group is said to be strictly simple if it has no proper nontrivial ascendant subgroups. That is, G {\displaystyle...

{\displaystyle \{A_{i}\}} by some simple group. The classification of finite simple groups gives us a complete list of finite simple groups; so the solution to the...

mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is...

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

Thompson during his work on finding all the minimal finite simple groups. The simple N-groups were classified by Thompson (1968, 1970, 1971, 1973, 1974...

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

special linear groups and alternating groups (these groups are all simple, as the alternating group over 5 or more letters is simple): L2(4) ≅ A5 L2(5)...