Search results
Results from the WOW.Com Content Network
The formal group ring of a formal group law is a cocommutative Hopf algebra analogous to the group ring of a group and to the universal enveloping algebra of a Lie algebra, both of which are also cocommutative Hopf algebras. In general cocommutative Hopf algebras behave very much like groups.
The definition of a group does not require that = for all elements and in . If this additional condition holds, then the operation is said to be commutative, and the group is called an abelian group. It is a common convention that for an abelian group either additive or multiplicative notation may be used, but for a nonabelian group only ...
In less formal terms, the group consists of words in the generators and their inverses, subject only to canceling a generator with an adjacent occurrence of its inverse. If G is any group, and S is a generating subset of G, then every element of G is also of the above form; but in general, these products will not uniquely describe an element of G.
A formal organization is an organization with a fixed set of rules of intra-organization procedures and structures. As such, it is usually set out in writing, with a language of rules that ostensibly leave little discretion for interpretation .
It is a group of people that often hang around each other. They can be like some clubs, but much less formal. They are usually known in many countries to cause social unrest and also have negative influence on the members and may be a target for the law enforcers in case of any social vices.
A formal group homomorphism from a formal group F to a formal group G is a power series over the same ring as the formal groups which has zero constant term and is such that: ((,)) = ((), ()) Consider a formal group F(X,Y) with coefficients in the ring of integers in a local field (for example Z p).
A corporate group is composed of companies. The general rule is that a company is a separate legal entity from its shareholders, that is the shareholder's liability for the subsidiary's debts is limited to the value of the shares, [4] and the shareholders cannot be required to perform the company's obligations.
The quest for informal group satisfaction may lead members away from formal organizational objectives. What is good for and desired by informal group members is not always good for the organization. Doubling the number of coffee breaks and the length of the lunch period may be desirable for group members but costly and unprofitable for the firm.