Normal generation of locally compact 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 کاملBracket Products on Locally Compact Abelian Groups
We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
متن کاملNormal subgroup structure of totally disconnected locally compact groups
The present article is a summary of joint work of the author and Phillip Wesolek on the normal subgroup structure of totally disconnected locally compact second-countable (t.d.l.c.s.c.) groups. The general strategy is as follows: We obtain normal series for a t.d.l.c.s.c. group in which each factor is ‘small’ or a non-abelian chief factor; we show that up to a certain equivalence relation (call...
متن کاملFrom Locally Compact Groups
Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...
متن کاملLocally compact abelian groups
These notes are a gloss on the first chapter of Walter Rudin’s Fourier Analysis on Groups, and may be helpful to someone reading Rudin. The results I do prove are proved in more detail than they are in Rudin. I caution that before reading the first chapter of that book it is know about the Gelfand transform on commutative Banach algebras because results from that are used without even stating t...
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: Bulletin of the London Mathematical Society
سال: 2013
ISSN: 0024-6093
DOI: 10.1112/blms/bdt009