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Longer titles found: Transitively normal subgroup (view), Quasinormal subgroup (view), C-normal subgroup (view), Weakly normal subgroup (view), Abnormal subgroup (view), Malnormal subgroup (view), Subnormal subgroup (view), Pronormal subgroup (view), Seminormal subgroup (view), Paranormal subgroup (view)

searching for Normal subgroup 55 found (393 total)

alternate case: normal subgroup

Hurwitz surface (645 words) [view diff] exact match in snippet view article find links to article

Fuchsian group of a Hurwitz surface is a finite index torsionfree normal subgroup of the (ordinary) (2,3,7) triangle group. The finite quotient group

presentation if it is isomorphic to the quotient of a free group on S by the normal subgroup generated by the relations R. As a simple example, the cyclic group

instance, a non-solvable CN-group G is such that its largest solvable normal subgroup O∞(G) is a 2-group, and the quotient is a group of even order. Solvable

primitive group of type SD on Δ with minimal normal subgroup Tl. Moreover, N = Tkl is a minimal normal subgroup of G and G induces a transitive subgroup of

is called the gauge group. In quantum gauge theory, one considers a normal subgroup G 0 ( X ) {\displaystyle G^{0}(X)} of a gauge group G ( X ) {\displaystyle

{\displaystyle {\mathcal {X}}} is not a simple group as it always contains the normal subgroup G {\displaystyle {\mathcal {G}}} . It was proved by Mather and Thurston

automorphisms preserving the direction of time. The group Aut+(II25,1) has a normal subgroup Ref generated by its reflections, whose simple roots correspond to

of units of the Hurwitz quaternions, which has order 24, contains a normal subgroup of order 8 isomorphic to the quaternion group, and is the binary tetrahedral

the normal subgroup of index 2 of Γ, consisting of elements that are the product of an even number of generators; and let Γ1 be the normal subgroup of

infinite ordinal, then G ω {\displaystyle G_{\omega }} is the smallest normal subgroup of G such that the quotient is residually nilpotent, that is, such

are isomorphic if the original group has a quotient by a discrete normal subgroup which is linear. For compact Lie groups, the complexification, sometimes

are isomorphic if the original group has a quotient by a discrete normal subgroup which is linear. For compact Lie groups, the complexification, sometimes

Leedham-Green (1994) and Shalev (1994). They are: Conjecture A: Every p-group has a normal subgroup of class 2 with index depending only on p and its coclass. Conjecture

of degree 3. The alternating group A 3 {\displaystyle A_{3}} is a normal subgroup of S 3 {\displaystyle S_{3}} , so we have the two subnormal series

Sarah (1996), "Computing matrix group decompositions with respect to a normal subgroup", Journal of Algebra, 184 (3): 818–838, doi:10.1006/jabr.1996.0286

Thompson's group F, and the quotient of Higman's group by a maximal proper normal subgroup, are not linear. By the corollary to the Tits alternative mentioned

Klein graph is the group PGL2(7) of order 336, which has PSL2(7) as a normal subgroup. This group acts transitively on its half-edges, so the Klein graph

continuous. The kernel of a representation ρ of a group G is defined as the normal subgroup of G whose image under ρ is the identity transformation: ker ⁡ ρ =

series (Hall 1940). A soluble A-group has a unique maximal abelian normal subgroup (Hall 1940). The Fitting subgroup of a solvable A-group is equal to

the middle column is not exact: C 2 {\displaystyle C_{2}} is not a normal subgroup in the semidirect product. Since A 5 {\displaystyle A_{5}} is simple

Capelli dated 1884. If G {\displaystyle G} is a finite group with normal subgroup H {\displaystyle H} , and if P {\displaystyle P} is a Sylow p-subgroup

unipotent elements in the radical of G. It is a connected unipotent normal subgroup of G, and contains all other such subgroups. A group is called reductive

… , a m {\displaystyle a_{1},\,a_{2},\,\ldots ,\,a_{m}} , by the normal subgroup R ⊂ F m {\displaystyle R\subset F_{m}} generated by the relations r

… , a m {\displaystyle a_{1},\,a_{2},\,\ldots ,\,a_{m}} , by the normal subgroup R ⊂ F m {\displaystyle R\subset F_{m}} generated by the relations r

of an algebraic group is called the identity component. It forms a normal subgroup. Kolchin, E. R., Differential Algebra and Algebraic Groups, Academic

respectively the left cosets as orbits under right translation. A normal subgroup of a topological group, acting on the group by translation action,

Let G be a one-relator group given by presentation (2). Then the normal subgroup N = ⟨ ⟨ r ⟩ ⟩ F ( X ) ≤ F ( X ) {\displaystyle N=\langle \langle r\rangle

Liebeck (1987) classified the ones with a regular elementary abelian normal subgroup Bannai (1971–72) classified the ones whose socle is a simple alternating

over the subgroups of G. (Note that H is not assumed here to be a normal subgroup of G, for while G/H is not a group in this case, it is still a G-set

Γ0(N)+ denote its quotient by positive scalar matrices. Then Γ0(N) is a normal subgroup of Γ0(N)+ of index 2s (where s is the number of distinct prime factors

two dimensional space of solutions. On the orientation-preserving normal subgroup, this two-dimensional representation corresponds to the monodromy of

x_{r})} into itself for some r ≤ n {\displaystyle r\leq n} . It has a normal subgroup given by the Cremona group of automorphisms of k ( x 1 , . . . , x

conjugation by elements of G {\displaystyle G} (generalizing the notion of a normal subgroup), and S {\displaystyle S} is Eulerian if for every s ∈ S {\displaystyle

{\displaystyle G} is the original group and N {\displaystyle N} is the normal subgroup; this is read " G {\displaystyle G} mod N {\displaystyle N} ", where

H} in G {\displaystyle G} . Moreover, if H {\displaystyle H} is a normal subgroup of G {\displaystyle G} , then any left transversal is also a right

inner structure group of the J-structure. It is a closed connected normal subgroup. Let K have characteristic not equal to 2. Let Q be a quadratic form

counterexamples: non-amenable finitely presented groups that have a periodic normal subgroup with quotient the integers. For finitely generated linear groups, however

matrices is exactly the derived subgroup, in other words the smallest normal subgroup such that the quotient by it is abelian. In other words, the Whitehead

isometries or multiply the metric by −1. The identity component has a normal subgroup R2 with quotient R, where R acts on R2 with 2 (real) eigenspaces, with

MCG(S)} of the diffeomorphism group of S {\displaystyle S} by the normal subgroup of those that are isotopic to the identity (the same definition can

finite index subgroup of E. It is called a normal layer if F is a normal subgroup of E, and a cyclic layer if in addition the quotient group is cyclic

is the only non-trivial normal subgroup of SL(2,k), so that PSL(2,k) = SL(2,k)/{±I} is simple. In fact if K is a normal subgroup, then the Bruhat decomposition

with P. H. Tiep: Characters of relative p'-degree with respect to a normal subgroup, Ann. of Math.178 (3) (2013), 1135–1171. doi:10.4007/annals.2013.178

the case, note that the kernel of p {\displaystyle p} is a discrete normal subgroup of G ~ {\displaystyle {\tilde {G}}} , which is therefore in the center

or minus the identity matrix. PSL(2,R) is contained as an index-two normal subgroup, the other coset being the set of 2×2 matrices with real entries whose

{\displaystyle \operatorname {Hol} _{p}^{0}(\omega )} (which is a normal subgroup of the full holonomy group). The discrete group Hol p ⁡ ( ω ) / Hol

{\displaystyle G} is virtually infinite cyclic if and only if it has a finite normal subgroup W {\displaystyle W} such that G / W {\displaystyle G/W} is either infinite

that each subgroup in the chain is normal in G {\displaystyle G} . A normal subgroup has been known since the 1940s to be left and (dual) right modular

The Hochschild–Serre spectral sequence relates the cohomology of a normal subgroup N of G and the quotient G/N to the cohomology of the group G (for (pro-)finite

of S {\displaystyle S} which are isotopic to the identity. It is a normal subgroup of the group of positive homeomorphisms, and the mapping class group

automorphisms of a Laguerre plane which fix each parallel class form a normal subgroup, the kernel of the full automorphism group. The 2 {\displaystyle 2}

interior of Ω1 iz a fundamental domain for G. Moreover, the index two normal subgroup G0 consisting of orientation-preserving mappings is a classical Schottky

_{1}(M_{n})\cong F_{n}} , and, moreover, up to a quotient by a finite normal subgroup isomorphic to Z 2 n {\displaystyle \mathbb {Z} _{2}^{n}} , the mapping

R:=\ker(\vartheta )} . Then R ◃ F {\displaystyle R\triangleleft F} is a normal subgroup of F {\displaystyle F} consisting of the defining relations for G ≃

Otto Hölder was "given two groups G and H, find all groups E having a normal subgroup N isomorphic to G such that the factor group E/N is isomorphic to H"