Group cohomology of special linear group:SL(2,5)
This article gives specific information, namely, group cohomology, about a particular group, namely: special linear group:SL(2,5).
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This article describes the group cohomology of special linear group:SL(2,5).
|Family name||Parameter values||General discussion of group cohomology of family|
|double cover of alternating group||degree , i.e., the group||group cohomology of double cover of alternating group|
|special linear group of degree two over a finite field of size||, i.e., field:F5, i.e., the group is||group cohomology of special linear group of degree two over a finite field|
Homology groups for trivial group action
FACTS TO CHECK AGAINST (homology group for trivial group action):
First homology group: first homology group for trivial group action equals tensor product with abelianization
Second homology group: formula for second homology group for trivial group action in terms of Schur multiplier and abelianization|Hopf's formula for Schur multiplier
General: universal coefficients theorem for group homology|homology group for trivial group action commutes with direct product in second coordinate|Kunneth formula for group homology
Over the integers
The homology groups over the integers are as follows:
The sequence of homology groups for positive degrees has a period of 4, which is in keeping with the fact that is a finite group with periodic cohomology, as are all special linear groups of degree two over a finite field.