mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup H of a group...

mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such...

2 elements. A large subgroup H (preferably a maximal subgroup) of the Monster is selected in which it is easy to perform calculations. The subgroup H chosen is...

torus subgroups, in particular by the maximal torus subgroups. A torus in a compact Lie group G is a compact, connected, abelian Lie subgroup of G (and...

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 has no maximal subgroups...

The maximal subgroups of Sn fall into three classes: the intransitive, the imprimitive, and the primitive. The intransitive maximal subgroups are exactly...

The Tits group occurs as a maximal subgroup of the Fischer group Fi22. The group 2F4(2) also occurs as a maximal subgroup of the Rudvalis group, as the...

p} . A Sylow p-subgroup (sometimes p-Sylow subgroup) of a finite group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup of G {\displaystyle...

elements of a maximal abelian subgroup. The normalizers of these maximal abelian subgroups turn out to be exactly the maximal proper subgroups of G. These...

mod 3, so is a subgroup of the Chevalley group E8(3). The subgroup preserving the Lie bracket (over the integers) is a maximal subgroup of the Thompson...

Dedekind eta function. Wilson (1999) found the 30 conjugacy classes of maximal subgroups of B which are listed in the table below. (Gorenstein 1993) Leon,...

Fitting subgroup, so the generalized Fitting subgroup is a central extension of a product of p-groups and simple groups. The layer is also the maximal normal...

is a maximal subgroup of the Lyons group. McL has one conjugacy class of involution (element of order 2), whose centralizer is a maximal subgroup of type...

element of the subgroup. For each idempotent e of the semigroup there is a unique maximal subgroup containing e. Each maximal subgroup arises in this...

G2(4) is in turn isomorphic to a subgroup of the Conway group Co1. There are 9 conjugacy classes of maximal subgroups of J2. Some are here described in...

· Suz of the Suzuki group. This makes the group 6 · Suz · 2 into a maximal subgroup of Conway's group Co0 = 2 · Co1 of automorphisms of the Leech lattice...

A003917 in the OEIS). Wilson (1985) found the 9 conjugacy classes of maximal subgroups of Ly as follows: Richard Lyons (1972,5) "Evidence for a new finite...

extension of M21 by the symmetric group S3. PΓL(3,4) has an embedding as a maximal subgroup of M24.(Griess 1998, p. 55) A hyperoval has no 3 points that are collinear...

algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example, in the general...

Artinian rings. The ACC is equivalent to the maximal condition: every non-empty collection of subgroups has a maximal member, and the DCC is equivalent to the...

and Yoshiara (1985) independently found the 13 conjugacy classes of maximal subgroups of O'N as follows: In 2017 John F. R. Duncan, Michael H. Mertens,...

quasithin groups. Wilson (1984) found the 15 conjugacy classes of maximal subgroups of Ru as follows: Griess (1982) Aschbacher, Michael; Smith, Stephen...

closed) field k {\displaystyle k} is the centralizer of a maximal torus. Cartan subgroups are smooth (equivalently reduced), connected and nilpotent...

function. Norton & Wilson (1986) found the 14 conjugacy classes of maximal subgroups of HN as follows: Harada, Koichiro (1976), "On the simple group F...

found the 11 conjugacy classes of maximal subgroups of He as follows: Butler, Gregory (1981), "The maximal subgroups of the sporadic simple group of Held"...

representations of M11 over any field. There are 5 conjugacy classes of maximal subgroups of M11 as follows: The maximum order of any element in M11 is 11....

(1966) found the 7 conjugacy classes of maximal subgroups of J1 shown in the table. Maximal simple subgroups of order 660 afford J1 a permutation representation...

of the monster vertex algebra. There are 11 conjugacy classes of maximal subgroups of M12, 6 occurring in automorphic pairs, as follows: The cycle shape...

Lie group of real dimension 496. This is simply connected, has maximal compact subgroup the compact form (see below) of E8, and has an outer automorphism...

related to the double cover of the subgroup M22. Magliveras (1971) found the 12 conjugacy classes of maximal subgroups of HS as follows: Traces of matrices...