- {\displaystyle {\begin{aligned}\bullet :(N\
rtimes _{\varphi }H)\times (N\
rtimes _{\varphi }H)&\to N\
rtimes _{\varphi }H\\(n_{1},h_{1})\bullet (n_{2}...
- {\displaystyle (\mathbb {Z} _{3}^{7}\times \mathbb {Z} _{2}^{11})\
rtimes \,((A_{8}\times A_{12})\
rtimes \mathbb {Z} _{2}).} The
largest group representation for...
- _{4}\
rtimes \mathbb {Z} _{2}} ditetragonal-pyramidal C4v
polar 8
dihedral D 8 = Z 4 ⋊ Z 2 {\displaystyle \mathbb {D} _{8}=\mathbb {Z} _{4}\
rtimes \mathbb...
-
Lorentz group, R 1 , 3 ⋊ O ( 1 , 3 ) , {\displaystyle \mathbf {R} ^{1,3}\
rtimes \operatorname {O} (1,3)\,,} with
group multiplication ( α , f ) ⋅ ( β ,...
- (3)\cong G_{2}\
rtimes G_{1}} G 4 ⊴ G 1 {\displaystyle G_{4}\trianglelefteq G_{1}} G 1 ≅ G 4 ⋊ G 3 {\displaystyle G_{1}\cong G_{4}\
rtimes G_{3}} S G a l...
- {\displaystyle (\mathbb {Z} _{3}^{7}\times \mathbb {Z} _{2}^{11})\
rtimes \,((A_{8}\times A_{12})\
rtimes \mathbb {Z} _{2}).} This
group can also be
described as...
-
crossed product by the dual
action ( A ⋊ G ) ⋊ Γ {\displaystyle (A\
rtimes G)\
rtimes \Gamma } .
Under this identification, the
double dual
action of G {\displaystyle...
-
isomorphic to ( Z 5 ⋊ φ Z 4 ) × ( Z 2 × Z 2 ) {\displaystyle (\mathbb {Z} _{5}\
rtimes _{\varphi }\mathbb {Z} _{4})\times (\mathbb {Z} _{2}\times \mathbb {Z} _{2})}...
- N\
rtimes H}
where N is
abelian and H is finite. (For example, any
generalized dihedral group.) Any
semidirect product N ⋊ H {\displaystyle N\
rtimes H}...
- such that N is a
normal subgroup of G, then G = N ⋊ H {\displaystyle G=N\
rtimes H} and G = H ⋉ N {\displaystyle G=H\ltimes N} mean that G is the semidirect...
