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Poset-blowdowns of generalized quaternion groups | ||
International Journal of Group Theory | ||
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 20 تیر 1402 اصل مقاله (10.68 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.137628.1841 | ||
نویسندگان | ||
Kenjiro Sasaki* 1؛ Shigeru Takamura1؛ Ryota Hirakawa2 | ||
1Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, JAPAN | ||
2Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, JAPAN | ||
چکیده | ||
Poset-blowdown of subgroup posets of groups is an analog of blowdown in algebraic geometry. It is a poset map obtained by contracting normal subgroups. For finite groups, this is considered as a map between the Hasse diagrams of the subgroup posets. Poset-blowdowns are classified into three types: \textit{tame, wild}, and \textit{hybrid} depending on the sizes of their fibers. In this paper we describe the poset-blowdowns for generalized quaternion groups $Q_{2^n}$ $(n \geq 3)$. They have distinguished nature in that all types (tame, wild, and hybrid) appear in the successive poset-blowdowns associated with the three chief series of $Q_{2^n}$. | ||
کلیدواژهها | ||
Subgroup poset؛ Hasse diagram؛ poset map؛ Frattini subgroup؛ chief series | ||
مراجع | ||
[1] Y. Chen and G. Chen, A note on a characterization of generalized quaternion 2-groups, C. R. Math. Acad. Sci. Paris, 352 no. 6 (2014) 459–461. | ||
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