The integral group ring ℤ⁢ G of a group G has only trivial central units if the only central
units of ℤ⁢ G are±z for z in the center of G. We show that the order of a finite solvable group …

Abstract The Gruenberg–Kegel graph of a group is the undirected graph whose vertices are
those primes which occur as the order of an element of the group, and distinct vertices p, q …

Groups whose non-linear irreducible characters are rational valued Page 1 Arch. Math. 94 (2010),
411–418 c© 2010 Birkhäuser / Springer Basel AG 0003-889X/10/050411-8 published online …

Let $ L/K $ be a finite Galois extension of number fields with Galois group $ G $. Let $ p $ be
a prime and let $ r\leq 0$ be an integer. By examining the structure of the $ p $-adic group …

Let G be a finite group and let Irr (G) be the set of all irreducible complex characters of G. For
a character χ∈ Irr (G), the number cod (χ):=| G: ker (χ)|/χ (1) is called the co-degree of χ. The …

Frobenius Q1-groups Page 1 Arch. Math. 105 (2015), 509–517 c© 2015 Springer Basel
0003-889X/15/060509-9 published online October 31, 2015 DOI 10.1007/s00013-015-0834-6 …

An element of a group G is called semi-rational if there is a natural number m such that each
generator of〈 x〉 belongs to the conjugacy class of G containing x or xm. If all elements of G …

Let $ G $ be a finite group and, for a given complex character $\chi $ of $ G $, let ${\mathbb
{Q}}(\chi) $ denote the field extension of ${\mathbb {Q}} $ obtained by adjoining all the …

Abstract Representation theory of finite groups has many important applications in the theory
of abstract groups. This theory was invented by George Frobenius more than 100 years ago …

RATIONAL NEARLY SIMPLE GROUPS Page 1 Bull. Aust. Math. Soc. 103 (2021), 475–485
doi:10.1017/S0004972720000969 RATIONAL NEARLY SIMPLE GROUPS FARIDEH …