摘要:不存在以散在單型Janko群J1作為本原自同構(gòu)群基柱的旗傳遞2-(v, k, λ)設(shè)計.
關(guān)鍵詞:Janko群; 群作用; 2-設(shè)計
中圖分類號:O152.1, O157.2? ?文獻標(biāo)示碼:A
對于具有傳遞性質(zhì)的2-(v, k, λ)設(shè)計的研究由來已久,早在1985年,Kantor就已經(jīng)對2-傳遞自同構(gòu)群作用下的2-(v, k, λ)對稱設(shè)計進行了完全分類[1].1988年,Zieschang給出了旗傳遞2-(v, k, λ)在(r, λ)=1時的自同構(gòu)群需要滿足的條件[2].2000年,Camina等人給出了線傳遞2-(v, k, λ)設(shè)計的自同構(gòu)群基柱不能為散在單群的結(jié)論[3].2015年,田德路和周勝林完全分類了散在單群作為自同構(gòu)群基柱的旗傳遞、點本原2-(v, k, λ)對稱設(shè)計[4].2017年,詹小秦和周勝林就散在單群基柱和λ≥(r, λ)2條件下的旗傳遞點本原非對稱設(shè)計展開了研究[5].本文繼續(xù)對2-設(shè)計的分類問題進行研究,討論散在單型Janko群J1作為本原自同構(gòu)群基柱的非平凡的旗傳遞2-(v, k, λ)設(shè)計的存在性問題,得到了如下定理:
基金項目支持:廣州市科技計劃項目(No:201804010088);廣東省特色創(chuàng)新類項目(No:2018KTSCX160).
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