کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4584960 | 1630510 | 2014 | 24 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Bass units as free factors in integral group rings of simple groups Bass units as free factors in integral group rings of simple groups](/preview/png/4584960.png)
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 ZGZG. It was recently proved that if G is solvable then there is a Bass unit or a bicyclic unit v and a positive integer n such that the group generated by unun and vnvn is a non-abelian free group. It has been conjectured that this holds for arbitrary groups G. To prove this conjecture it is enough to do it under the assumption that G is simple and a is a dihedral p-critical element in G. We first classify the simple groups with a dihedral p -critical element. They are all of the form PSL(2,q)PSL(2,q). We prove the conjecture for p=5p=5; for p>5p>5 and q even; and for p>5p>5 and q+1=2pq+1=2p. We also provide a sufficient condition for the conjecture to hold for p>5p>5 and q odd. With the help of computers we have verified the sufficient condition for all q<10000.
Journal: Journal of Algebra - Volume 404, 15 February 2014, Pages 100–123