Simple group information

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...

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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...

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...

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...

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...

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...

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...

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...

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

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...

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...

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

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 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...

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...

smallest non-abelian simple group, having order 60, and the smallest non-solvable group. The group A4 has the Klein four-group V as a proper normal subgroup...

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)...

linear group GL(n, C), and it has as a subgroup the special unitary group, consisting of those unitary matrices with determinant 1. In the simple case n...

classification of finite simple groups. For a prime number p {\displaystyle p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G {\displaystyle G}...

classification of finite simple groups, five is the count of exceptional Lie groups as well as the number of Mathieu groups that are sporadic groups. Five is also...

matrices which represent the groups. In Cartan's classification of the simple Lie algebras, the Lie algebra of the complex group Sp(2n, C) is denoted Cn,...

discussed in automorphism group, below. For n ≥ 5, Sn is an almost simple group, as it lies between the simple group An and its group of automorphisms. Sn...

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...