Abstract
A finite group G is called a Schur group if any S-ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. We prove that the groups Z3 × Z3n, where n ≥ 1, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur p-group, where p is an odd prime, is isomorphic to Z3 × Z3 × Z3 or Z3 × Z3n, n ≥ 1.
Original language | English |
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Article number | 1750045 |
Number of pages | 29 |
Journal | Journal of Algebra and its Applications |
Volume | 16 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Mar 2017 |
Keywords
- Cayley schemes
- Permutation groups
- S -rings
- Schur groups
- Srings