Locally cyclic group information

locally cyclic group is a group (G, *) in which every finitely generated subgroup is cyclic. Every cyclic group is locally cyclic, and every locally cyclic...

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...

element is called cyclic. Every infinite cyclic group is isomorphic to the additive group of the integers Z. A locally cyclic group is a group in which every...

subgroup is cyclic. Every cyclic group is locally cyclic, and every finitely-generated locally cyclic group is cyclic. Every locally cyclic group is abelian...

In abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order n, every subgroup's order is a divisor of...

number theory, locally compact abelian groups are abelian groups which have a particularly convenient topology on them. For example, the group of integers...

abelian group Group representation Klein four-group List of small groups Locally cyclic group Nilpotent group Non-abelian group Solvable group P-group Pro-finite...

{Z} ,n\in \mathbb {N} .} Hausdorff completion Locally cyclic group Pro-p group – type of profinite groupPages displaying wikidata descriptions as a fallback...

locally finite group is a group for which every finitely generated subgroup is finite. Since the cyclic subgroups of a locally finite group are finitely...

to a locally partially ordered space is studied in Roll (1993); see also Directed topology. A cyclically ordered group is a set with both a group structure...

integers (with the addition operation) is the "only" infinite cyclic group. Some groups can be proven to be isomorphic, relying on the axiom of choice...

quotient group. Subgroups, quotients, and direct sums of abelian groups are again abelian. The finite simple abelian groups are exactly the cyclic groups of...

group Abelian group Torsion subgroup Free abelian group Finitely generated abelian group Rank of an abelian group Cyclic group Locally cyclic group Solvable...

In number theory, the Hasse norm theorem states that if L/K is a cyclic extension of number fields, then if a nonzero element of K is a local norm everywhere...

mathematics, a Baer group is a group in which every cyclic subgroup is subnormal. Every Baer group is locally nilpotent. Baer groups are named after Reinhold...

duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative...

point Lie group – Group that is also a differentiable manifold with group operations that are smooth Locally compact field Locally compact group – topological...

unity. The Brauer group Br(R) of the field R of real numbers is the cyclic group of order two. There are just two non-isomorphic real division algebras...

for groups of the same size. For example, three groups of size 120 are the symmetric group S5, the icosahedral group A5 × Z / 2Z and the cyclic group Z...

a cyclically ordered group is a set with both a group structure and a cyclic order, such that left and right multiplication both preserve the cyclic order...

equal to this diameter). Another simple example is given by the infinite cyclic group Z {\displaystyle \mathbb {Z} } : the Cayley graph of Z {\displaystyle...

character group for finite abelian groups is in number theory, where it is used to construct Dirichlet characters. The character group of the cyclic group also...

finite number of discrete groups is discrete. a discrete group is compact if and only if it is finite. every discrete group is locally compact. every discrete...

profinite topology on G. A group is residually finite if, and only if, its profinite topology is Hausdorff. A group whose cyclic subgroups are closed in...

In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant...

n we have a covering group of the circle by itself T → T that sends z to zn. The kernel of this homomorphism is the cyclic group consisting of the nth...

Compact groups or locally compact groups — Many of the results of finite group representation theory are proved by averaging over the group. These proofs...

setting by James Arthur. Finally arithmetic groups are often used to construct interesting examples of locally symmetric Riemannian manifolds. A particularly...