where Φ(f) is the number of residue classes in D˜ modulo f which consist of numbers relatively prime to f (Φ is analogous to the Euler φ-function), and ef is the index of the group of units of the order Df in the group of units of the maximal order D˜. 12. A number ...
Functors on finite vector spaces and units in Abelian group rings If A is an elementary abelian group, let U (A) denote the group of units, modulo torsion, of the group ring Z [A]. We study U (A) by means of the composite... K Hoechsmann - Canadian mathematical bulletin = Bulleti...
Lee showed that there exists an isomorphism between the p-primary part of the ideal class group and p-primary part of the unit group modulo cyclotomic unit group in Q(zeta p(n))(+) for all sufficiently large n under some conditions. In the present paper, we shall give an analogue of ...
n (Mathematics) a group the defined binary operation of which is commutative: ifaandbare members of an Abelian group thenab=ba [C19: named after Niels HenrikAbel(1802–29), Norwegian mathematician] Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publisher...
We give a finite set of generators for a subgroup of finite index of the unit group of an integral group ring of an Hamiltonian group the order of which is only divisible by 2 and primes that are congruent to 3 modulo 8. An application is given to the unit group of the integral group...
(b) Find all of the normal subgroup of D_6. Find all group homomorphisms: a. \mathbb{Z}_6 \to K_4, where K_4 is the Klein group, b. \mathbb{Z}_3 \to A_4. Show that the set {5, 15, 25, 35} is a group under ...
Let G be a finite group, u a Bass unit based on an element a of G of prime order, and assume that u has infinite order modulo the centre of the units of the integral group ring ZG. It was recently proved that if G is solvable then there is a Bass unit or a bicyclic unit v ...
There, the authors studied countably generated projective modules that are finitely generated modulo the Jacobson radical and showed that they appear in a wide variety of situations. Our aim here is to introduce an object {\mathrm S}(R) that can also be built out of countably generated ...
Let us view ℤ3 as the additive group of remainders modulo 3, whose elements are 1̲, 0̲, and −1̲. The group Aut(ℤ3) consists of two elements, namely, id and −id. Naturally, gluing via id will yield the trivial bundle over 𝑆1, i.e., the bundle B is isomorp...
An element z ∈ S is called a zero element (or simply a zero) if sz = z = zs ∀s ∈ S. Example 2. Any group is clearly its own group of units (groups by definition have inverses). Z4 = {0, 1, 2, 3} equipped with multiplication modulo 4 isa monoid with group of units ...