Considering subsets of an irreducible root system that are

abelian, Lawther classifies all maximal

abelian sets--that is,

abelian sets properly contained in no other--up to the action of Coxeter group W: for each W-orbit of maximal

abelian sets, he provides an explicit representation X, identifies the (setwise) stabilizer WX of X in W, and decomposes the X into WX-orbits.

Abelian anyons have been detected and play a major role in the fractional quantum Hall effect.

Examples of such groups are: finite

Abelian groups ([12], Theorem 4.

The main motivation for our initial work [LP15b] was the case H = C[G] for G

abelian, as treated in the second authors joint paper [FPSV14].

by [5], A5 is the smallest non

abelian simple group of order 22 .

It is clear that (NQ, +) is an

abelian group and (NQ,.

Genus theory for number fields was first studied for quadratic,

abelian, and Galois extensions over Q by Hasse, Iyanaga Tamagawa and Leopoldt, and Frohlich.

Real

abelian fields satisfying the Hilbert-Speiser condition for some small primes p .

These results on Euclidean self-dual cyclic codes have been generalized to

abelian codes in group algebras [6] and the complete characterization and enumeration of Euclidean self-dual

abelian codes in principal ideal group algebras (PIGAs) have been established.

They discuss modules, including vector spaces and

abelian groups, group theory, and quasigroups.

The reason to establish such differences is that the electron is usually described through Quantum Electrodynamics (QED) [8], an

abelian field theory.

distinguished for his many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry), the Serre-Tate theorem in algebraic geometry, says that under certain conditions an

abelian scheme (an projective algebraic variety that is also an algebraic group, i.