Hochschild cohomology of the integral group ring of the semidihedral group

2012 ◽  
Vol 183 (5) ◽  
pp. 640-657
Author(s):  
A. I. Generalov
2011 ◽  
Vol 18 (02) ◽  
pp. 241-258 ◽  
Author(s):  
Takao Hayami

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.


2018 ◽  
Vol 28 (02) ◽  
pp. 257-290
Author(s):  
Takao Hayami

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].


1990 ◽  
Vol 42 (3) ◽  
pp. 383-394 ◽  
Author(s):  
Frank Röhl

In [5], Roggenkamp and Scott gave an affirmative answer to the isomorphism problem for integral group rings of finite p-groups G and H, i.e. to the question whether ZG ⥲ ZH implies G ⥲ H (in this case, G is said to be characterized by its integral group ring). Progress on the analogous question with Z replaced by the field Fp of p elements has been very little during the last couple of years; and the most far reaching result in this area in a certain sense - due to Passi and Sehgal, see [8] - may be compared to the integral case, where the group G is of nilpotency class 2.


2000 ◽  
Vol 43 (1) ◽  
pp. 60-62 ◽  
Author(s):  
Daniel R. Farkas ◽  
Peter A. Linnell

AbstractLet G be an arbitrary group and let U be a subgroup of the normalized units in ℤG. We show that if U contains G as a subgroup of finite index, then U = G. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.


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