Split and Minimal Abelian Extensions of Finite Groups
نویسندگان
چکیده
منابع مشابه
On component extensions locally compact abelian groups
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
متن کاملFINITE EXTENSIONS OF MINIMAL TRANSFORMATION GROUPS ( i )
In this paper we shall study homomorphisms p: W — Y on minimal transformation groups. We shall prove, in the case that W and Y are metrizable, that W is a finite (iV-to-1) extension of Y if and only if W is an Nfold covering space of Y and pisa covering map. This result places no further restrictions on the acting group. We shall then use this characterization to investigate the question of lif...
متن کاملFinite $p$-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 the Cohomology of Split Extensions of Finite Groups
Let G = HoQ be a split extension of nite groups. A theorem of Charlap and Vasquez gives an explicit description of the di erentials d2 in the Lyndon-Hochschild-Serre spectral sequence of the extension with coe cients in a eld k. We generalize this to give an explicit description of all the dr (r 2) in this case. The generalization is obtained by associating to the group extension a new twisting...
متن کاملCombinable Extensions of Abelian Groups
The design of decision procedures for combinations of theories sharing some arithmetic fragment is a challenging problem in verification. One possible solution is to apply a combination method à la Nelson-Oppen, like the one developed by Ghilardi for unions of non-disjoint theories. We show how to apply this non-disjoint combination method with the theory of abelian groups as shared theory. We ...
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: Transactions of the American Mathematical Society
سال: 1972
ISSN: 0002-9947
DOI: 10.2307/1996353