Hochschild Cohomology Ring of an Order of a Simple Component of the Rational Group Ring of the Generalized Quaternion Group

2008 ◽  
Vol 36 (7) ◽  
pp. 2785-2803
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Rational Group ◽  
Quaternion Group ◽  
Hochschild Cohomology Ring ◽  
Simple Component ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

On the Structure of Augmentation Quotient Groups for the Generalized Quaternion Group

2012 ◽  
Vol 19 (01) ◽  
pp. 137-148 ◽  
Author(s):  
Qingxia Zhou ◽  
Hong You
Keyword(s):  
Group Ring ◽  
Integral Group Ring ◽  
Augmentation Ideal ◽  
Integral Group ◽  
Quaternion Group ◽  
Generalized Quaternion Group ◽  
Augmentation Quotient ◽  
Generalized Quaternion ◽  
Quotient Groups

For the generalized quaternion group G, this article deals with the problem of presenting the nth power Δn(G) of the augmentation ideal Δ (G) of the integral group ring ZG. The structure of Qn(G)=Δn(G)/Δn+1(G) is obtained.

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].

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