x
uploads/normalizer.jpg

normalizer n.標準化者,歸一化者,規格化者。

normally

In this aspect , kondrat ' ev [ ll ] has shown that a group g is 2 - nilpotent if the normalizer of each sylow subgroup of g is of odd index in g . in 1995 , zhang [ 13jhas proved that a group g is soluble if the index of the normalizer of every sylow subgroup in g is a prime power 1988年, kondrat ’ ev卜11證明了:如果群g的任意西洛子群的正規化子在g中的指數為奇數,則g是2一冪零的。 1995年, zhang卜習證明了如果群g的任意西洛子群的正規化子有素數冪指數,則g是可解的。

In 1996 , guo [ 9 ] has further proved that the index of the normalizer of every sylow subgroup of g is an odd number or a prime if and only if g is a soluble group and g = kh , where k and h are the hall subgroups of g , k is a nilptent subgroup which is normal in a 2 ' - nilpotent . in this paper , we shall study the nilpotent length of finite groups whose sylow normalizer indices are of prime powers 1996年,郭文彬教授沙1證明了一個群g的西洛子群的正規化子的指數為奇數或為一個素數冪當巨僅當g為可解群而且g二尤廳,其中k和h都是群g的hall一子群, k是正規于g的一個2 ’一月恤21子群的冪零子群, h是2一冪零群。

Theorem 2 . 4 let g be a non - abelian inner - finite group , each non - trivial proper subgroup of g is prime order cyclic group if and only if g is a simple group ; each proper subgroup of g is nilpotent ; and each non - trivial subgroup of g is self - normalizer 4設g是非阿貝爾的內有限群,則g的每個非平凡真子群都是素數階循環群的充分必要條件是g是單群, g的每個真子群冪零且g的每個非平凡的真子群自正規化定理2

We note that in all the above papers , the groups are finite groups whose normalizers of sylow subgroups have some given internal properties 我們注意到在上述的所有文獻中,都是對西洛子群的揚州大學碩士學位論文生正規化子的內部性質進行討論的有限群。

It is well known that the normalizers of sylow subgroups of a finite group play a crucial role in the investigation of finite groups 眾所周知,有限群的西洛子群的正規化子在對有限群g的研究中起著極其重要的作用。

Let be a class of groups . then , we denote by n the class of groups whose normalizers of all sylow subgroups are in 我們令x表示一個群類,我們把西洛子群的正規化子包含在x中的群構成的群類用n ~ x來表示。

Haiyan lanfon normalizer co . , ltd is located in the fastener district of china , haiyan zhejiang province 海鹽聯豐標準件廠位于中國緊固件之鄉?浙江海鹽,距上海98公里,杭州80公里,地理優勢明顯,交通便捷。

On the other hand , one can also study the finite groups whose normalizers of sylow subgroups have some given external properties 另一方面,人們也可以討論西洛子群的正規化子有某種外部性質的有限群。