In mathematics, in the realm of group theory, an IA automorphism of a group is an automorphism that acts as identity on the abelianization.[1] The abelianization of a group is its quotient by its commutator subgroup. An IA automorphism is thus an automorphism that sends each coset of the commutator subgroup to itself.
The IA automorphisms of a group form a normal subgroup of the automorphism group. Every inner automorphism is an IA automorphism.
^Bachmuth, S. (1966), "Induced automorphisms of free groups and free metabelian groups", Transactions of the American Mathematical Society, 122: 1–17, doi:10.2307/1994498, MR 0190212.
commutator subgroup. An IAautomorphism is thus an automorphism that sends each coset of the commutator subgroup to itself. The IAautomorphisms of a group form...
quotientable automorphism. Under a quotient map, class automorphisms go to class automorphisms. Every class automorphism is an IAautomorphism, that is,...
ISSN 0002-9904. Bachmuth, Seymour; Mochizuki, Horace Y. (1978-11-01). "IA-automorphisms of the free metabelian group of rank 3". Journal of Algebra. 55 (1):...
the identity map IA on A, yielding a morphism g such that gf=IA. As a result, g is a surjective morphism and hence an automorphism, and then f is necessarily...
and φ {\displaystyle \varphi } is a group homomorphism from N to the automorphism group of H, then N ⋊ φ H = H ⋉ φ N {\displaystyle N\rtimes _{\varphi...
gt and adjoints g ↦ g*. The structure group contains the automorphism group. The automorphism group can be identified with the stabilizer of 1 in the structure...
Fourier transform is an automorphism on the Schwartz space, as a topological vector space, and thus induces an automorphism on its dual, the space of...
_{2}} . But Z 2 {\displaystyle \mathrm {Z} _{2}} has only the trivial automorphism, so the only semi-direct product of N {\displaystyle N} and G / N {\displaystyle...
associate of an element b if a divides b and b divides a. automorphism A ring automorphism is a ring isomorphism between the same ring; in other words...
construction of the Griess algebra that has the monster group as its automorphism group. This monster vertex algebra was also used to prove the monstrous...
{\displaystyle 7d} . All automorphisms of a Laguerre plane which fix each parallel class form a normal subgroup, the kernel of the full automorphism group. The 2...
permutations preserving the set system is used to build the automorphisms of the graph. An automorphism permutes the vertices of a graph; in other words, it...
because although charge conjugation is an automorphism of the gamma group, it is not an inner automorphism (of the group). Conjugating matrices can be...
may conclude that each α {\displaystyle {\boldsymbol {\alpha }}} is an automorphism of a subspace of the cotangent space defined by orthogonality with respect...
and following the presentation of his Habilitation thesis on stable automorphism groups, a post as Privatdozent, or full professor. Finally, in 1955,...
Global Information