کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6414160 | 1630441 | 2017 | 26 صفحه PDF | دانلود رایگان |

We prove that the group algebra KG of a group G over a field K is primitive, provided that G has a non-abelian free subgroup with the same cardinality as G, and that G satisfies the following condition (â): for each subset M of G consisting of a finite number of elements not equal to 1, and for any positive integer m, there exist distinct a, b, and c in G so that if (x1â1g1x1)â¯(xmâ1gmxm)=1, where gi is in M and xi is equal to a, b, or c for all i between 1 and m, then xi=xi+1 for some i. This generalizes results of [1,9,17], and [18], and proves that, for every countably infinite group G satisfying (â), KG is primitive for any field K. We use this result to determine the primitivity of group algebras of one relator groups with torsion.
Journal: Journal of Algebra - Volume 473, 1 March 2017, Pages 221-246