Finite near-fields with hereditary non-abelian groups |
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| Author | |
| Abstract |
A multiplicative group is said to be hereditary non-abelian if either it is abelian or every its non--abelian subgroup is isomorphic to the multiplicative group of some near-field. A complete classification of hereditary non-abelian groups of finite near-fields is obtained.
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| Keywords |
hereditary non-abelian group, near-field, isomorphism
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| DOI |
doi:10.30970/ms.34.1.38-43
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Reference |
1. L.E. Dixon, Definitions of a group and a field by independent postulates, Trans. Amer. Math. Soc. 6 (1905), 198--204.
2. S. Ligh, Finite Hereditary Near-field groups, Mh. Math. 86 (1978), 7-11. 3. G.A. Miller, H. Moreno, Non-abelian groups in which every subgroup is abelian, Trans. Amer. Math. Soc. 4 (1903), 398-404. 4. H. Wahling, Theorie der Fastkörper, Essen: Thales Verlag, 1987. 5. H. Zassenhaus, Über endliche Fastkörper, Ab. Math. Sem. Univ. Hamburg, 11 (1935/36), 187-220. 6. K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. Phys., 3 (1892), 265–284. 7. М. Холл, Теория групп, М.: Издательство иностранной литературы, 1962, 468 с. |
| Pages |
38-43
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| Volume |
34
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| Issue |
1
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| Year |
2010
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| Journal |
Matematychni Studii
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| Full text of paper | |
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