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Solvable intransitive permutation groups with constant movement | ||
| Journal of Mahani Mathematical Research | ||
| دوره 14، شماره 1 - شماره پیاپی 31، فروردین 2025، صفحه 155-163 اصل مقاله (485.67 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23569.1666 | ||
| نویسندگان | ||
| Mehdi Rezaei* 1؛ Mehdi Alaeiyan2؛ Zeinab Foruzanfar1 | ||
| 1Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran | ||
| 2Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran | ||
| چکیده | ||
| In this paper, all solvable intransitive permutation groups with constant movement are classified and we show that they are one of the following groups: a cyclic $p$-group, an elementary abelian $p$-group, a Frobenius group of order 12 or a Frobenius group of order $pq$, where $p$ and $q$ are primes such that $p=q(q-1)+1.$ | ||
| کلیدواژه‌ها | ||
| Permutation group؛ orbit؛ constant movement؛ Frobenius group | ||
| مراجع | ||
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[1] Alaeiyan, M., & Rezaei, M. (2011). Intransitive permutation groups with bounded movement having maximum degree. Math. Rep., 13(63)(2), 109-115.
[2] Alaeiyan, M., & Tavallaee, H. A. (2009). Permutation groups with the same movement. Carpathian J. Math., 25(2), 147-156.
[3] Alaeiyan, M., & Yoshiara, S. (2005). Permutation groups of minimal movement. Arch. Math., 85, 211-226. https://doi.org/10.1007/s00013-005-1337-7
[4] Foruzanfar, Z., & Rezaei, M. (2022, February). 2-transitive permutation groups with abelian stabilizers having constant movement, 14th Iranian International Group Theory Conference, Tehran, Iran.
[5] Foruzanfar, Z., & Rezaei, M. (2022, February). Primitive permutation groups with constant movement, 14th Iranian International Group Theory Conference, Tehran, Iran.
[6] Gorenstein, D. (1980). Finite Groups. Second Edition. Chelsea, New York.
[7] Hassani. A., Khayaty (Alaeiyan), M., Khukhro, E. I., & Praeger, C. E. (1999). Transitive permutation groups with bounded movement having maximal degree. J. Algebra, 214, 317-337. https://doi.org/10.1006/jabr.1998.7681
[8] Praeger, C. E. (1991). On permutation groups with bounded movement. J. Algebra, 144, 436-442. https://doi.org/10.1016/0021-8693(91)90114-n
[9] Shi, W. J., & Lv, H. (2017). A Note of CP2 Groups. Commun. Math. Stat., 5, 447-451. https://doi.org/10.1007/s40304-017-0121-x | ||
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