發(fā)布時(shí)間：2018-04-13 21:40

  本文選題：可裂性 + 正規(guī)子群　； 參考：《中北大學(xué)學(xué)報(bào)(自然科學(xué)版)》2017年01期

【摘要】：研究了一個(gè)有限群何時(shí)在某個(gè)正規(guī)子群上可裂的問(wèn)題,推廣了著名的Huppert可裂性定理,主要把Huppert可裂性定理中討論的p-版本推廣到π-版本并對(duì)其進(jìn)行了詳細(xì)的證明,從而得到一個(gè)更為廣泛的證明可裂性的判據(jù).其證明引用了經(jīng)典的Gaschütz可裂性定理,運(yùn)用了傳輸同態(tài),采用了由特殊到一般的證明思路.最后,作為對(duì)該定理的實(shí)際應(yīng)用,給出了若干經(jīng)典的傳輸定理的統(tǒng)一的簡(jiǎn)化證明.
[Abstract]:In this paper, the problem of when a finite group can be split on a normal subgroup is studied, and the famous Huppert cleavage theorem is generalized. The p- version discussed in the Huppert cleavage theorem is extended to 蟺-version and proved in detail.Thus, a more extensive criterion to prove the cleavability is obtained.The proof uses the classical Gasch 眉 tz cleavage theorem, uses the transmission homomorphism, and adopts the proof idea from special to general.Finally, as a practical application of the theorem, a unified simplified proof of some classical transmission theorems is given.
【作者單位】： 山西大學(xué)數(shù)學(xué)科學(xué)學(xué)院;
【基金】：山西省自然科學(xué)基金資助項(xiàng)目(201601D011006)
【分類號(hào)】：O152.1
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本文編號(hào)：1746293