"Hall divisor" redirects here. For the physical parameter, see quantum Hall effect.
In mathematics, specifically group theory, a Hall subgroup of a finite group G is a subgroup whose order is coprime to its index. They were introduced by the group theorist Philip Hall (1928).
theory, a Hallsubgroup of a finite group G is a subgroup whose order is coprime to its index. They were introduced by the group theorist Philip Hall (1928)...
as "H is a subgroup of G". The trivial subgroup of any group is the subgroup {e} consisting of just the identity element. A proper subgroup of a group...
In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...
{\displaystyle p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup of G {\displaystyle...
Three subgroups lemma Hall algebra, and Hall polynomials HallsubgroupHall–Higman theorem Hall–Littlewood polynomial Hall's universal group Hall's marriage...
of group theory, a Carter subgroup of a finite group G is a self-normalizing subgroup of G that is nilpotent. These subgroups were introduced by Roger...
group theory, the Frattini subgroup Φ ( G ) {\displaystyle \Phi (G)} of a group G is the intersection of all maximal subgroups of G. For the case that G...
product Sylow theorems Hallsubgroup Wreath product Butterfly lemma Center of a group Centralizer and normalizer Characteristic subgroup Commutator Composition...
subgroup of G {\displaystyle G} admits a unique smooth structure which makes it an embedded Lie subgroup of G {\displaystyle G} —i.e. a Lie subgroup such...
Serpentine subgroup (part of the kaolinite-serpentine group in the category of phyllosilicates) are greenish, brownish, or spotted minerals commonly found...
In mathematics, specifically group theory, a subgroup H of a group G may be used to decompose the underlying set of G into disjoint, equal-size subsets...
abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced...
abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order n, every subgroup's order is a divisor of n...
604800 as a subgroup of SL(6,4)", Journal of Algebra 11 (1969), 455–460. Wales, David B., "Generators of the Hall–Janko group as a subgroup of G2(4)",...
theorem states that every group G {\displaystyle G} is isomorphic to a subgroup of the symmetric group on (the underlying set of) G {\displaystyle G} ...
discrete if and only if its identity is isolated. A subgroup H of a topological group G is a discrete subgroup if H is discrete when endowed with the subspace...
theory, the omega and agemo subgroups described the so-called "power structure" of a finite p-group. They were introduced in (Hall 1933) where they were used...
2-rank 2. Alperin showed that the Sylow subgroup must be dihedral, quasidihedral, wreathed, or a Sylow 2-subgroup of U3(4). The first case was done by the...
ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant det...
group G, one can form the subgroup that consists of all its integer powers: ⟨g⟩ = { gk | k ∈ Z }, called the cyclic subgroup generated by g. The order...
solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof...
specifically group theory, the three subgroups lemma is a result concerning commutators. It is a consequence of Philip Hall and Ernst Witt's eponymous identity...
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