scholarly journals Hochschild cohomology of the integral group ring of the dihedral group. I: Even case

2008 ◽  
Vol 19 (5) ◽  
pp. 723-763
Author(s):  
A. I. Generalov
Keyword(s):  
Group Ring ◽  
Dihedral Group ◽  
Hochschild Cohomology ◽  
Integral Group Ring ◽  
Integral Group ◽  
Group I

On the automorphism group of the integral group ring of the infinite dihedral group

1988 ◽  
Vol 108 (1-2) ◽  
pp. 1-10
Author(s):  
D. A. R. Wallace
Keyword(s):  
Automorphism Group ◽  
Normal Subgroup ◽  
Group Ring ◽  
Polynomial Ring ◽  
Dihedral Group ◽  
Integral Group Ring ◽  
Integral Group ◽  
Index 2 ◽  
Skolem Theorem ◽  
Inner Automorphisms

SynopsisLet ℤ(G) be the integral group ring of the infinite dihedral groupG; the aim is to calculate Autℤ(G), the group of Z-linear automorphisms of ℤ(G). It is shown that Aut ℤ(G), the subgroup of Aut *ℤ(G) consisting of those automorphisms that preserve elementwise the centre of ℤ(G), is a normal subgroup of Aut *ℤ(G) of index 2 and that Aut*ℤ(G) may be embedded monomorphically intoM2(ℤ[t]), the ring of 2 × 2 matrices over a polynomial ring ℤ[t]From this embedding and by the Noether—Skolem Theorem it is shown that Inn (G), the group of inner automorphisms of ℤ(G) induced by the units of ℤ(G), is a normal subgroup of Aut*ℤ(G)/ such that Aut*ℤ(G)/Inn (G) is isomorphic to the Klein four-group.

Hochschild Cohomology Ring of the Integral Group Ring of the Semidihedral 2-Group

2011 ◽  
Vol 18 (02) ◽  
pp. 241-258 ◽  
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Integral Group Ring ◽  
Integral Group ◽  
Hochschild Cohomology Ring

We determine the ring structure of the Hochschild cohomology HH*(ℤ G) of the integral group ring of the semidihedral 2-group G = SD2r of order 2r.

On Hochschild cohomology ring and integral cohomology ring for the semidihedral group

2018 ◽  
Vol 28 (02) ◽  
pp. 257-290
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Integral Group Ring ◽  
Integral Group ◽  
Precise Description ◽  
Arbitrary Integer ◽  
Integral Cohomology ◽  
Hochschild Cohomology Ring

We will determine the ring structure of the Hochschild cohomology [Formula: see text] of the integral group ring of the semidihedral group [Formula: see text] of order [Formula: see text] for arbitrary integer [Formula: see text] by giving the precise description of the integral cohomology ring [Formula: see text] and by using a method similar to [T. Hayami, Hochschild cohomology ring of the integral group ring of the semidihedral [Formula: see text]-group, Algebra Colloq. 18 (2011) 241–258].

Sign in / Sign up

Export Citation Format

Share Document