Cohomology of finite groups and elementary Abelian subgroups
نویسندگان
چکیده
منابع مشابه
Finite $p$-groups and centralizers of non-cyclic abelian subgroups
A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq Z(G)$. In this paper, we give a complete classification of finite $mathcal{CAC}$-$p$-groups.
متن کاملOn non-normal non-abelian subgroups of finite groups
In this paper we prove that a finite group $G$ having at most three conjugacy classes of non-normal non-abelian proper subgroups is always solvable except for $Gcong{rm{A_5}}$, which extends Theorem 3.3 in [Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable, Acta Math. Sinica (English Series) 27 (2011) 891--896.]. Moreover, we s...
متن کاملCohomology of groups, abelian Sylow subgroups and splendid equivalences
Let G be a finite group and let R be a complete discrete valuation domain of characteristic 0 with residue field k of characteristic p and let S be R or k. The cohomology rings H∗(K,S) for subgroups K of G together with restriction to subgroups of G, transfer from subgroups of G and conjugation by elements of G gives H∗(−, S) the structure of a Mackey functor. Moreover, the group HSplenS(K) of ...
متن کاملCharacteristic Subgroups of Finite Abelian Groups
We consider the question: When do two finite abelian groups have isomorphic lattices of characteristic subgroups? An explicit description of the characteristic subgroups of such groups enables us to give a complete answer to this question in the case where at least one of the groups has odd order. An “exceptional” isomorphism, which occurs between the lattice of characteristic subgroups of Zp ×...
متن کاملLarge Abelian Subgroups of Finite p-Groups
It would be interesting to extend this result by allowing B to have nilpotence class 2 instead of necessarily being abelian. This cannot be done if p = 2 (Example 4.2), but perhaps it is possible for p odd. (It was done by the author ([Gor, p.274]; [HB, III, p.21]) for the special case in which p is odd and [B,B] ≤ A.) However, there is an application of Thompson’s Replacement Theorem that can ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology
سال: 1972
ISSN: 0040-9383
DOI: 10.1016/0040-9383(72)90017-1