Access the full text.
Sign up today, get DeepDyve free for 14 days.
B. Huppert (1967)
Endliche Gruppen I
Sudesh Shankar (2019)
Group TheoryComputers, Rigidity, and Moduli
R. Dark, C. Scoppola (1996)
On Camina Groups of Prime Power OrderJournal of Algebra, 181
Sugandha Maheshwary (2016)
Integral Group Rings With All Central Units Trivial: Solvable GroupsIndian Journal of Pure and Applied Mathematics, 49
I. Isaacs, M. Lewis (2014)
CAMINA p-groups that are generalized Frobenius complementsArchiv der Mathematik, 104
S. Alavi, A. Daneshkhah, M. Darafsheh (2016)
On semi-rational Frobenius groupsJournal of Algebra and Its Applications, 15
Ron Brown, D. Harrison (1998)
Abelian Frobenius kernels and modules over number ringsJournal of Pure and Applied Algebra, 126
E. Soares (1986)
Big primes and character values for solvable groupsJournal of Algebra, 100
E. Jespers, Á. Río (2015)
Orders and Generic Constructions of Units
R. Gow (1976)
Groups whose characters are rational-valuedJournal of Algebra, 40
(2016)
The GAP Group
J. Ritter, S. Sehgal (1990)
Integral group rings with trivial central units, 108
Peter Cameron, Michael Giudici, Gareth Jones, William Kantor, Mikhail Klin, D. Marušič (2019)
PERMUTATION GROUPSGroup Theory for Physicists
Joan Tent (2012)
Quadratic rational solvable groupsJournal of Algebra, 363
D. Chillag, S. Dolfi (2010)
Semi-rational solvable groups, 13
M. Darafsheh, H. Sharifi (2004)
Frobenius $ \mathbb Q $ -groupsArchiv der Mathematik, 83
AbstractThe integral group ring ℤG{\mathbb{Z}G}of a group G has only trivial central units if the only central units of ℤG{\mathbb{Z}G}are ±z{\pm z}for z in the center of G. We show that the order of a finite solvable group G with this property can only be divisible by the primes 2, 3, 5 and 7, by linking this to inverse semi-rational groups and extending one result on this class of groups. We also classify the Frobenius groups whose integral group rings have only trivial central units.
Forum Mathematicum – de Gruyter
Published: Jul 1, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.