On Schur p-Groups of odd order Full article
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Journal of Algebra and its Applications
ISSN: 0219-4988 |
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| Output data | Year: 2017, Volume: 16, Number: 3, Article number : 1750045, Pages count : 29 DOI: 10.1142/S0219498817500451 | ||
| Tags | Permutation groups, Cayley schemes; S-rings, Schur groups | ||
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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.
Cite:
Ryabov G.
On Schur p-Groups of odd order
Journal of Algebra and its Applications. 2017. V.16. N3. 1750045 :1-29. DOI: 10.1142/S0219498817500451 WOS Scopus OpenAlex
On Schur p-Groups of odd order
Journal of Algebra and its Applications. 2017. V.16. N3. 1750045 :1-29. DOI: 10.1142/S0219498817500451 WOS Scopus OpenAlex
Dates:
| Submitted: | Nov 10, 2015 |
| Accepted: | Feb 16, 2016 |
| Published online: | Apr 4, 2016 |
Identifiers:
| Web of science: | WOS:000398858300005 |
| Scopus: | 2-s2.0-84962719367 |
| OpenAlex: | W2198053984 |