鎶ュ憡棰樼洰錛欼somorphism classes of regular subgroups in the holomorph of a finite group
銆€銆€鎶ュ憡浜猴細(xì)鏇懼杽璋婏紙涓北澶у銆佺壒鑱樼爺絀跺憳錛?br>銆€銆€鎶ュ憡鏃墮棿錛?019騫?0鏈?1鏃ワ紙鍛ㄥ洓錛?4錛?0
銆€銆€鎶ュ憡鍦扮偣錛氭牸涓?00瀹?br>銆€銆€鎽樿錛歀et N be a finite group and write Hol(N) for its holomorph. Regular subgroups G of Hol(N) are closely related to Hopf-Galois structures on field extensions as well as non-degenerate set-theoretic solutions to the Yang-Baxter equation. Therefore, there has been a growing interest in the study of these regular subgroups G. A natural question which arises is: Are there any restrictions on the isomorphism class of G in relation to N? In this talk, we shall discuss some known results and open problems regarding this question.
銆€銆€鎶ュ憡浜虹畝浠嬶細(xì)
銆€銆€鏇懼杽璋婏紝涓北澶у鏁板瀛﹂櫌錛堢彔嫻鳳級(jí)鐗硅仒鐮旂┒鍛樸€?016騫村湪緹庡浗鍔犲窞澶у鍦ｅ鑺姯鎷夊垎鏍¤幏鏁板鍗氬＋瀛︿綅錛屽甯堜負(fù)Adebisi Agboola鏁欐巿銆?016騫村埌2018騫村湪娓呭崕澶у涓樻垚妗愭暟瀛︾瀛︿腑蹇?jī)鋼Q鍗氬＋鍚庛€?017騫磋幏鍗氬＋鍚庣瀛﹀熀閲戠壒鍒祫鍔╋紝2019騫磋幏楂樻牎鍩烘湰縐戠爺涓氬姟璐逛腑灞卞ぇ瀛﹂潚騫存暀甯堝煿鑲查」鐩紝浠ュ強(qiáng)鍥藉鑷劧鍩洪噾闈掑勾鍩洪噾銆傜爺絀舵柟鍚戜負(fù)浠ｆ暟鏁拌鍜岀兢璁猴紝涓昏鐮旂┒鏁存暟鐜殑浼界綏鐡︽ā緇撴瀯錛屼互鍙?qiáng)鏈夐檺缇ょ殑鍏ㄥ舰閲岀殑姝ｅ垯瀛惥煠銆傚湪Bull. London Math. Soc., Proc. Amer. Math. Soc., Pacific J. Math., J. Algebra絳夊浗闄呮€х殑鏉傚織涓€鍏卞彂琛ㄤ簡(jiǎn)12綃囪鏂囷紝鍏朵腑10綃囨槸鐙珛钁椾綔銆?br>銆€銆€嬈㈣繋騫垮ぇ甯堢敓鍙傚姞錛?/p>
鐞嗗闄?br>2019騫?0鏈?0鏃?/p>
