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山东大学学报（理学版） 2024年第6期59卷 103-107页

作者：李艳霞海进科青岛大学数学与统计学院山东青岛266071

设G为有限群,F=A×Fr为有限生成交换群,其中A是有限的,Fr为自由交换群,证明F到G的同态数量是|A|与|G|最大公因子的倍数,推广著名的***定理。

关键词：群同态群作用自由交换群

On the isomorphisms of the character rings

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Science China Mathematics 2005年第1期48卷 88-96页

作者： hai jinke Department of Mathematics Qingdao UniversityQingdao 266071China

By considering the Galois action and the group action,we give the relation of two isomorphism character rings on the arbitrary field K with CharK = *** results generalize Saksonov's theorem.

关键词： algebra isomorphism,character ring,primitive idempotent.

Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups

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Algebra Colloquium 2021年第4期28卷 561-568页

作者： jinke hai Lele Zhao College of Mathematics and Statistics Qingdao University QingdaoShandong 266071China

Let G be an extension of a finite characteristically simple group by an abelian group or a finite simple *** is shown that every Coleman automorphism of G is an inner *** in such automorphisms arises from the study of... 详细信息

关键词： characteristically simple group Coleman automorphism normalizer property

On Coleman Automorphisms of Extensions of Finite Quasinilpotent Groups by Some Groups

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Algebra Colloquium 2018年第2期25卷 181-188页

作者： jinke hai Yixin Zhu College of Mathematics and Statistics Qingdao University Qingdao Shandong 266071 China School of Mathematical Science Capital Normal University Beijing 100048 China

Let G be an extension of a finite quasinilpotent group by a finite group. It is shown that under some conditions every Coleman automorphism of G is an inner automorphism. The interest in such automorphisms arose from ... 详细信息

关键词： semidirect product Coleman automorphisms normalizer property

On Coleman automorphisms of wreath products of finite nilpotent groups by abelian groups

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Science China Mathematics 2011年第10期54卷 2253-2257页

作者： hai jinke LI ZhengXing College of Mathematics Qingdao University Qingdao 266071 China

Let G = NwrA be a wreath product of a finite nilpotent group N by an abelian group A. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result,it is obtaine... 详细信息

关键词： Coleman automorphisms wreath products the normalizer problem

Class-Preserving Coleman Automorphisms of Finite Groups Whose Second Maximal Subgroups Are TI-Subgroups

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Journal of Mathematical Research with Applications 2013年第2期33卷 241-245页

作者： Zhengxing LI jinke hai College of Mathematics Qingdao University

Recall that a subgroup H of a finite group G is called a TI-subgroup if H ∩ Hg= 1 or H for each g ∈ *** that G is a finite group whose second maximal subgroups are *** is shown that every class-preserving Coleman automorphism of G is an inner *** an immediate consequence of this result,we obtain that the normalizer property holds for G.

关键词： normalizer property Coleman automorphism class-preserving automorphism.

ON COLEMAN OUTER AUTOMORPHISM GROUPS OF FINITE GROUPS

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Acta Mathematica Scientia 2014年第3期34卷 790-796页

作者：海进科李正兴 School of Mathematics Qingdao University

Let G be a finite group and Outcoz（G） the Coleman outer automorphism group of G（for the definition, see below）. The question whether Outcol（G） is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol（G） to be a p＇-group are obtained. Our results generalize some well-known theorems.

关键词： Coleman automorphisms Frattini subgroups generalized Fitting subgroups

Coleman Automorphisms of Finite Groups with a Unique Nontrivial Normal Subgroup

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Journal of Mathematical Research with Applications 2014年第3期34卷 301-306页

作者： Zhengxing LI jinke hai Shuxian YANG College of Mathematics Qingdao University

Let G be a finite group with a unique nontrivial normal subgroup. It is shown that every Coleman automorphism of G is an inner automorphism.

关键词： Coleman automorphism minimal normal subgroup.

The extension of the first main theorem for π-blocks

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Science China Mathematics 2006年第5期49卷 620-625页

作者： hai jinke Department of Mathematics, Qingdao University, Qingdao 266071, China College of mathematics ,Shandong University, Jinan 250100, China Department of Mathematics Qingdao University Qingdao China College of mathematics Shandong University Jian China

Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.

关键词： π-block, π-separable group, π-regular classes, defect group.

Geochronology,Geochemistry,and Sr-Nd-Hf Isotopes of the Diorite Porphyrites from the Weining Beishan Area,Ningxia Hui Autonomous Region:Constraints on Their Source and Tectonic Implications

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Journal of Earth Science 2024年第2期35卷 462-475页

作者： Anlu Liu Lianfu hai jinke Liu Xiaojun Zhang haifeng Li Fengshun Zhao Guoliang Zhao Jinhe Bai Yifu Museum China University of GeosciencesWuhan430074China School of Earth Resources China University of GeosciencesWuhan430074China Mineral Geological Survey Institute of Ningxia Hui Autonomous Region Yinchuan750021China National Demonstration Center for Experimental Mineral Exploration Education China University of GeosciencesWuhan430074China Coal Geological Survey Institute of Ningxia Hui Autonomous Region Yinchuan750021China Zhuhai Engineering Investigation Institute of Guangdong Province Zhuhai519000China

The Weining Beishan area of Ningxia Hui Autonomous Region is located at on the western edge of the Helanshan tectonic belt,which is a tectonic joint among Alxa Block,Ordos Block,and North Qilian orogenic ***,the tectonic evolution of this area remains unclear due to the lack of magmatic *** paper conducted researches on geochronology,geochemistry,and Sr-Nd-Hf isotopes of the diorite porphyrites exposed in the Weining Beishan *** zircon U-Pb dating yields two ages of 145.0±1.1 and 146.2±1.5 Ma,and the whole-rock geochemical data indicate that the diorite porphyrites are metaluminous to weakly peraluminous and high-K calc-alkaline *** characteristics of highly initial^(87)Sr/^(86)Sr ratios(0.70816 to 0.71047),negativeε_(Nd)(t)(−8.9 to−8.4),and negativeε_(Hf)(t)(−13.8 to−21.2)indicate that the diorite porphyrites originated from partial melting of the middle-lower ancient crust related to the North China *** with the regional geology,we suggested that partial melting was triggered by a tectonic activity of deep faults cutting through the crust under the regional stress transformation from compressing to extension during the Late Jurassic–Early Cretaceous,which is probably related to the westward subduction of the Paleo-Pacific Plate.

关键词： zircon U-Pb dating Sr-Nd-Hf isotopes magma source diorite porphyrite Weining Beishan area Ningxia Hui Autonomous Region geochronology geochemistry