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)...

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...

abelian subgroups of |G|. This pattern of partitioning the prime divisors of |G| according to conjugacy classes of certain Hall subgroups (a Hall subgroup is...

{\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 Hall subgroup Hall–Higman theorem Hall–Littlewood polynomial Hall's universal group Hall's marriage...

{\displaystyle G/N} . An alternative statement of the theorem is that any normal Hall subgroup N {\displaystyle N} of a finite group G {\displaystyle G} has a complement...

graph. The Hall–Janko graph was originally constructed by D. Wales to establish the existence of the Hall-Janko group as an index 2 subgroup of its automorphism...

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...

product Sylow theorems Hall subgroup Wreath product Butterfly lemma Center of a group Centralizer and normalizer Characteristic subgroup Commutator Composition...