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The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups | ||
| International Journal of Group Theory | ||
| مقاله 21، دوره 8، شماره 4، اسفند 2019، صفحه 1-3 اصل مقاله (164.59 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2018.110074.1472 | ||
| نویسنده | ||
| Julian Brough* | ||
| Fachgruppe Mathematik und Informatik, BU Wuppertal, Wuppertal, Germany | ||
| چکیده | ||
| We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers. Insoluble groups which satisfy the one-prime power hypothesis have been classified. However it has remained an open question whether the one-prime power hypothesis is inherited by normal subgroups and quotients groups. In this note we construct examples to show the one-prime power hypothesis is not necessarily inherited by normal subgroups or quotient groups. | ||
| کلیدواژهها | ||
| Conjugacy classes؛ finite groups؛ restriction to substructures | ||
| مراجع | ||
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[1] A. R. Camina and R. D. Camina, One-prime p ower hyp othesis for conjugacy class sizes, Int. J. Group Theory , 6 no. 3 (2017) 13{19. [2] N. Du and M. L. Lewis, The prime-p ower hyp othesis and solvable groups, Arch. Math. (Basel) , 109 no. 4 (2017) 301-303 [3] Y. Liu and X. Song and J. Zhang, Nonsolvable groups satisfying the prime-p ower hyp othesis, J. Algebra , 442 (2015) 455{483. [4] B. Taeri, Cycles and bipartite graph on conjugacy class of groups, Rend. Semin. Mat. Univ. Padova , 123 (2010) 233{247. | ||
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