multiplicative group

Consider the multiplicative group of positive real numbers (R, ).

This follows, in part, since the multiplicative group of complex numbers C is connected.

The multiplicative group of a ring, especially when the ring is a field.

Let now be a multiplicative group of order .

One can either focus on the whole multiplicative group or on the subgroup.

The multiplicative group of the complex numbers is divisible.

In fact, the multiplicative group of the non-residues and 1 form the Klein four-group.

The S-units form a multiplicative group containing the units of R.

Interaction between the multiplicative groups of the two adelic structures is part of higher class field theory.

A primitive element of a finite field is a generator of the field's multiplicative group.

The associated character of the multiplicative group (Z/k) is the principal character which always takes the value 1.

More generally, for any ring R, the units in R form a multiplicative group.

In a commutative ring the invertible elements, or units, form an abelian multiplicative group.

More generally, every finite subgroup of the multiplicative group of any field is cyclic.

In mathematics and group theory, the term multiplicative group refers to one of the following concepts:

If 'T' is the multiplicative group, then this gives the restriction of scalars a permutation module structure.

Such matrices form a multiplicative group.

The corresponding result for the multiplicative group is known as Hilbert's Theorem 90, and was known before 1900.

Consider the multiplicative group .

All operations are performed modulo a prime , or in other words, in the multiplicative group .

It is a method to represent elements of a subgroup of a multiplicative group of a finite field.

The circle group forms a subgroup of C, the multiplicative group of all nonzero complex numbers.

The modular function is a continuous group homomorphism into the multiplicative group of nonzero real numbers.

Importantly, the DDH assumption does not hold in the multiplicative group , where is prime.

The exponential function uniformizes the exponential map of the multiplicative group .