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1. Subgroup: A non-empty subset $H$ of a group $G$ which itself is a group with respect to the operation defined on $G$. A subset $H$ of a group $G$ is a subgroup of $G$ if and only if: 1) $H ... (Mathematics) [100%] 2024-01-26
2. Subgroup: In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗. More precisely, H is a ... (Subset of a group that forms a group itself) [100%] 2024-01-26 [Group theory] [Subgroup properties]...
3. Subgroup: In group theory, a subgroup of a group is a subset which is itself a group with respect to the same operations. Formally, a subset S of a group G is a subgroup if it satisfies the following conditions: These ... [100%] 2023-10-25
4. Subgroup: A non-empty subset $H$ of a group $G$ which itself is a group with respect to the operation defined on $G$. A subset $H$ of a group $G$ is a subgroup of $G$ if and only if: 1) $H ... (Mathematics) [100%] 2023-10-21
5. Subgroup: In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗. More precisely, H is a ... (Subset of a group that forms a group itself) [100%] 2023-12-30 [Group theory] [Subgroup properties]...
6. Supagroup: Supagroup es una banda de Hard Rock estadounidense proveniente de Nueva Orleans, Louisiana, Estados Unidos. Su alineación consiste en el vocalista y guitarrista Chris Lee, el guitarrista Benji Lee, el bajista Brewer Brian Broussard y el baterista Leon Touzet.​ Chris ... [74%] 2024-01-26
7. Supagroup: Supagroup es una banda de Hard Rock estadounidense proveniente de Nueva Orleans, Louisiana, Estados Unidos. Su alineación consiste en el vocalista y guitarrista Chris Lee, el guitarrista Benji Lee, el bajista Brewer Brian Broussard y el baterista Leon Touzet.​ Chris ... [74%] 2023-12-29
8. Verbal subgroup: The subgroup $ V( G) $ of a group $ G $ generated by all possible values of all words (cf. Word) of some set $ V = \{ {f _ \nu ( x _ {1} \dots x _ {n _ \nu } ) } : {\nu \in I } \} $, when $ x _ ... (Mathematics) [70%] 2023-10-17
9. Characteristic subgroup: A subgroup of a group $G$ that is invariant under all automorphisms of $G$. Examples of characteristic subgroups are the centre of a group, denoted by $Z(G)$, the Fitting subgroup, $F(G)$, the commutator subgroup, $D(G)$, $[G,G ... (Mathematics) [70%] 2023-10-17
10. Parabolic subgroup: A parabolic subgroup of a linear algebraic group $G$ defined over a field $k$ is a subgroup $P\subset G$, closed in the Zariski topology, for which the quotient space $G/P$ is a projective algebraic variety. A subgroup $P ... (Mathematics) [70%] 2023-12-30
11. Subgroup system: A set $ \mathfrak A $ of subgroups (cf. Subgroup) of a group $ G $ satisfying the following conditions: 1) $ \mathfrak A $ contains the unit subgroup $ 1 $ and the group $ G $ itself; and 2) $ \mathfrak A $ is totally ordered by inclusion, i.e. (Mathematics) [70%] 2023-10-24
12. Commutator subgroup: The commutator subgroup of a group $G$, also called the derived group, second term of the lower central series, of $G$, is the subgroup of $G$ generated by all commutators of the elements of $G$ (cf. Commutator). (Mathematics) [70%] 2023-08-16
13. Congruence subgroup: In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example would be invertible 2 × 2 integer matrices of determinant 1, in which the off ... (Matrix group) [70%] 2023-04-16 [Modular forms] [Discrete groups]...
14. Puig subgroup: In mathematical finite group theory, the Puig subgroup, introduced by Puig (1976), is a characteristic subgroup of a p-group analogous to the Thompson subgroup. If H is a subgroup of a group G, then LG(H) is the subgroup ... [70%] 2023-12-02 [Finite groups]
15. Subgroup series: A subgroup series of a group $G$ is a finite chain of subgroups of $G$ contained in each other: $$E=G_0\subseteq G_1\subseteq \cdots \subseteq G_n=G\label{1}$$ or $$G=G_1\supseteq G_2\supseteq \cdots \supseteq G_{n ... (Mathematics) [70%] 2023-12-29
16. Frattini subgroup: In group theory, the Frattini subgroup is the intersection of all maximal subgroups of a group. Formally, where M runs over all maximal subgroups of G. [70%] 2023-09-10
17. Verbal subgroup: The subgroup $ V( G) $ of a group $ G $ generated by all possible values of all words (cf. Word) of some set $ V = \{ {f _ \nu ( x _ {1} \dots x _ {n _ \nu } ) } : {\nu \in I } \} $, when $ x _ ... (Mathematics) [70%] 2024-01-26
18. Characteristic subgroup: A subgroup of a group $G$ that is invariant under all automorphisms of $G$. Examples of characteristic subgroups are the centre of a group, denoted by $Z(G)$, the Fitting subgroup, $F(G)$, the commutator subgroup, $D(G)$, $[G,G ... (Mathematics) [70%] 2024-01-26
19. Parabolic subgroup: A parabolic subgroup of a linear algebraic group $G$ defined over a field $k$ is a subgroup $P\subset G$, closed in the Zariski topology, for which the quotient space $G/P$ is a projective algebraic variety. A subgroup $P ... (Mathematics) [70%] 2024-01-26
20. Subgroup series: A subgroup series of a group $G$ is a finite chain of subgroups of $G$ contained in each other: $$E=G_0\subseteq G_1\subseteq \cdots \subseteq G_n=G\label{1}$$ or $$G=G_1\supseteq G_2\supseteq \cdots \supseteq G_{n ... (Mathematics) [70%] 2024-01-26