Maximal elementary abelian subgroups



In this page we list the maximal elementary abelian subgroups of the group G (up to conjugacy). For each of these (representatives of conjugacy classes of) maximal elementary abelian subgroups, we provide its order, a list of generators in the group G, a table describing the restriction map, and another table describing the transfer map. We also give generators of the kernel of the restriction. At the bottom of this page we describe the nilradical of the cohomology ring, which can also be accessed directly using the "Nilradical" link. If you want to find the web page of the group isomorphic to a certain maximal elementary abelian subgroup, simply go to the group of that order with Hall-Senior number one.





Subgroup E number 1
This maximal elementary abelian subgroup is generated by the following element(s): g4 , g3 g4
This maximal elementary abelian subgroup has order 4




The following table describes the restriction to this maximal elementary abelian subgroup. Each row of the table has a generator of the cohomology ring of the group G, followed by its image (in the cohomology ring of the maximal elementary abelian subgroup) under the restriction map.



Generator of cohomology Image under restriction
z 0
y y
x 0
w z4 + z2 y2


The ideal of the kernel of the restriction is generated by the element(s) z , x




The following table describes the transfer map from this maximal elementary abelian subgroup. Each row of the table has a generator of the cohomology ring of the maximal elementary abelian subgroup as a module over the cohomology ring of the group G, followed by its image (in the cohomology ring of the group) under the tranfer map.



Generator of H*(E) as H*(G) module Image under transfer
z z
z2 0
z3 x




The last table in this page contains information about the nilradical of the cohomology ring of the group. This table can be accessed directly via the "Nilradical" link.



The kernel of the restriction to E is also the nilradical of P
It is nilpotent of degree 2