An application of blocks to torsion units in group rings

Abstract

We use the theory of blocks of cyclic defect to prove that under a certain condition on the principal p-block of a finite group G the normalized unit group of the integral group ring of G contains an element of order pq if and only if so does G, for q a prime different from p. Using this we verify the Prime Graph Question for all alternating and symmetric groups and also for two sporadic simple groups.

arXiv comment[v3] 8 pages, incorporated referee's comments, to appear in Proc. of the AMS

References in corpus (4)

• On the Prime Graph Question for Integral Group Rings of 4-primary groups II
• Rational conjugacy of torsion units in integral group rings of non-solvable groups
• On the Prime Graph Question for Integral Group Rings of 4-primary groups I
• On the Prime Graph Question for Almost Simple Groups with an Alternating Socle