»ù±¾ÊÍÒå:

×Ôͬ¹¹Èº

ÍøÂçÊÍÒå

1)automorphism group,×Ôͬ¹¹Èº

2)automorphism,×Ôͬ¹¹Èº

3)Automorphism groups,×Ôͬ¹¹Èº

4)group of automorphisms,×Ôͬ¹¹Èº

5)outer automorphism group,Íâ×Ôͬ¹¹Èº

6)groups of all automorphisms,È«×Ôͬ¹¹Èº

Ó÷¨ºÍÀý¾ä

An analysis of sub-simple properties of automorphism groups by a computer;

×Ôͬ¹¹ÈºµÄ´Îµ¥ÐÔ·ÖÎö¼°¼ÆËã»úʵÏÖ

The orders of automorphism groups of some families p-groups;

ijһÀà¼Ò×åp-ȺµÄ×Ôͬ¹¹ÈºµÄ½×(Ó¢ÎÄ)

In this paper, we determine explicitly the automorphism of filirom Lie algebra W6, the solvable Lie algebra with nilradical W6, and prove that this solvable Lie algebra has no nontrivial (non-constant) invariant.

ÎÄÕÂÈ·¶¨ÁËfiliformÀî´úÊýW6µÄ×Ôͬ¹¹Èº,È·¶¨ÁËÒÔW6Ϊnil-¸ù»ùµÄ¿É½âÀî´úÊý¼°ÆäΨһÐÔ,²¢ÇÒÖ¤Ã÷ÁËÕâÀà¿É½âÀî´úÊýûÓзÇƽ·²(¼´·Ç³£Êý)²»±äÁ¿¡£

A finite p-group G is called LA-group, if the order of G pides the order of the automorphism group of G.

³ÆÓÐÏÞp-ȺGÊÇLA-Ⱥ,Èç¹ûȺGµÄ½×ÄÜÕû³ýȺGµÄ×Ôͬ¹¹ÈºµÄ½×¡£

Abstract:Let G be a soluble block-transitive automorphism group of 2-(56,7,1) design D.

ÉèGÊÇÉè¼Æ2-(5~6,7,1)µÄÒ»¸ö¿É½âÇø´«µÝ×Ôͬ¹¹Èº,ÔòGÊÇÆì´«µÝµÄÇÒG¡öA¡öL(1,5~6)¡£

Holomorphic vectors and holomorphic automorphism groups of a sort of three-dimensional Hopf manifold;

Ò»ÀàÈýάHopfÁ÷ÐεÄ×Ôͬ¹¹ÈººÍÈ«´¿ÏòÁ¿³¡

In this paper,The order of automorphism groups of metacyclic inner abelian p-groups are determined when p¡Ù2,and the structure of automorphism groups are also given.

±¾ÎÄÈ·¶¨ÁËÑÇÑ­»·µÄÄÚ½»»»p-Ⱥ(p¡Ù2)µÄ×Ôͬ¹¹ÈºµÄ½×,²¢¸ø³öÁËÆä×Ôͬ¹¹ÈºµÄ½á¹¹¡£

Meanwhile,the formula about number of order on the group of automorphisms over finitely generated module over Ring Fq[x] is deduced.

ÔÚÌØÕ÷Ϊ2µÄÓòF2Éϸø³ön½×¾ØÕóΪƽ·½¾ØÕóµÄ³äÒªÌõ¼þ,´Ó¶ø¿Ì»®ÁËƽ·½¾ØÕóµÄÌØÕ÷,Çó³ö»·Fq[x]ÉÏÓÐÏÞÉú³ÉÄ£µÄ×Ôͬ¹¹ÈºµÄ½×Êý¹«Ê½,Óɴ˵õ½F2ÉÏÈ«Ìåƽ·½¾ØÕóµÄ¼ÆÊý¹«Ê½¡£

And their automorphism group sand outer automorphism groups are determined.

¶ÔÈÎÒâÆæËØÊýp,ÒýÈëÁËÒ»ÀàËùνµÄËãÊõp-Ⱥ,²¢È·¶¨ÁËÆä×Ôͬ¹¹ÈººÍÍâ×Ôͬ¹¹Èº,ËùµÃ½á¹ûÍƹã¾ßÓÐÒ»¸öÑ­»·¼«´ó×ÓȺµÄp-ȺµÄÏàÓ¦½áÂÛ¡£

The outer automorphism group of the free product of two syclic groups is constructed, and two exact formulas for calculating its order are established.

¾ßÌåµØ¹¹Ôì³öÁ½¸öÓÐÏÞÑ­»·ÈºµÄ×ÔÓÉ»ýµÄÍâ×Ôͬ¹¹Èº£¬²¢¸ø³öÁËÆä½×µÄ¼ÆË㹫ʽ¡£

A formula of the order of the outer automorphism group of a semidirect product is obtained,which can be applied to the investigation of the triviality of the outer automorphism group.

ÉèÓÐÏÞȺ G=Ný¡ HΪ°ëÖ±»ý ,±¾ÎĽèÖúÓÚ NºÍ HµÄ×Ôͬ¹¹Çó³öÁË GµÄÍâ×Ôͬ¹¹Èº½×µÄ¹«Ê½ ,²¢¸ø³öÁËÈô¸ÉÓ¦Óá£

According to the property and structure of generalized quaternion groups,using the methods of the extension theory of groups,the groups of all automorphisms of generalized quaternion group Q 4p and Q 4pm for odd prime p are determined,and the general structure of that of Q 4n deduced from that of Q 4p and Q 4pm is as follows:Suppose that p 1 is the smallest prime pisor of n,and n=p r .

¸ù¾Ý¹ãÒåËÄԪȺ Q4 nµÄ½á¹¹ºÍÐÔÖÊ ,ÀûÓÃȺµÄÀ©ÕÅÀíÂÛ ,ÏÈÈ·¶¨ÁË Q4 pÓë Q4 pmµÄÈ«×Ôͬ¹¹ÈºµÄ½á¹¹ ,Óɴ˹éÄɳöÒ»°ãµÄ¹ãÒåËÄԪȺ Q4 nµÄÈ«×Ôͬ¹¹ÈºµÄ½á¹¹ÈçÏ :Éè p1 Ϊ nµÄ×îСËØÒò×Ó ,n=pr1 1 pr22 ¡­ prkk Ϊ nµÄËØÊý·Ö½â ,ÄÇô(a)µ± p1 >2ʱ ,Aut(G) =¡´¦Á¡µ:(¡´¦Ç1 ¡µ¡Á¡´¦Ç2 ¡µ¡Á¡­¡Á¡´¦Çk¡µ) ;(b)µ± p1 =2ʱ ,Aut(G) =¡´¦Á¡µ:(¡´¦Ç2 ¡µ¡Á¡­¡Á¡´¦Çk¡µ) , r1 =1¡´¦Á¡µ:(¡´¦Ã¡µ¡Á¡´¦Ç2 ¡µ¡Á¡­¡Á¡´¦Çk¡µ) , r1 =2¡´¦Á¡µ:(¡´¦Ì¡µ¡Á¡´¦Í¡µ¡Á¡´¦Ç2 ¡µ¡Á¡­¡Á¡´¦Çk¡µ) , r1 ¡Ý 3¡£

The Construction of Group G with Automorphism Group A(G) of Order 2p

×Ôͬ¹¹ÈºA(G)µÄ½×Ϊ2pµÄȺGµÄ½á¹¹

LA-Group and the Stractore of Auto-Morphism Groups of Some Special p-Groups;

Èô¸ÉLA-Ⱥ¼°Ò»ÀàÌØÊâP-Ⱥ×Ôͬ¹¹ÈºµÄ½á¹¹

The order of the automorphism group of finite abelian group

ÓÐÏÞ½»»»ÈºµÄ×Ôͬ¹¹ÈºµÄ½×(Ó¢ÎÄ)

The Finite Groups of which the Automorphism Group s Order is 2¡«3p¡«2;

¾ßÓÐ2¡«3p¡«2½××Ôͬ¹¹ÈºµÄÓÐÏÞȺ

The Orders of Automorphism Groups of Groups of Order P¡«6 (¦Õ_(11),¦Õ_(33));

P¡«6½×ȺµÄ×Ôͬ¹¹ÈºµÄ½×£¨¦Õ_£¨11£©,¦Õ_£¨33£©£©

THE ORDERS OF AUTOMORPHISM GROUPS OF GROUPS OF ORDER p5;

p¡«5½×ȺµÄ×Ôͬ¹¹ÈºµÄ½×£¨¦µ_6¡ª¦µ_£¨10£©£©

Finite Nilpotent Groups with Automorphism Group of Order 4p~3

¾ßÓÐ4p~3½××Ôͬ¹¹ÈºµÄÓÐÏÞÃÝÁãȺ

Finite nilpotent groups with automorphism group of order 4p~2q

¾ßÓÐ4p~2q½××Ôͬ¹¹ÈºµÄÓÐÏÞÃÝÁãȺ

A New Series of LA-Groups and the Order of Their Automorphism Groups

һϵÁÐеÄLA-Ⱥ¼°Æä×Ôͬ¹¹ÈºµÄ½×

Approach of Calculating the Order of Automorphism Group of p-Group

¼ÆËãÓÐÏÞp-ȺµÄ×Ôͬ¹¹Èº½×µÄ·½·¨

An Action from Automorphism Group on Actor Group to Characteristic Group

×Ôͬ¹¹Èºµ½¶ÔÌØÕ÷×ÓȺµÄÉÌȺÉÏÒ»×÷ÓÃ

On the Autmorphism Groups of Metacyclic p-group with a Cyclic Maximal Subgroup

¾ßÓÐÑ­»·¼«´ó×ÓȺµÄÑÇÑ­»·p-ȺµÄ×Ôͬ¹¹Èº

The Order of Automorphism Group of the Group of Order p¡«6 (¦Õ_(14),¦Õ_(15),¦Õ_(22));

p¡«6½×Ⱥ£¨¦Õ_£¨14£©,¦Õ_£¨15£©,¦Õ_£¨22£©µÄ×Ôͬ¹¹ÈºµÄ½×

In other words it has a large automorphism group.

»»ÑÔÖ®£¬ËüÓдóµÄ×Ôͬ¹¹Èº¡£

Derivation Algebra and Automorphism Group of F[x,y];

´úÊýF[x£¬y]µÄµ¼×Ó´úÊýºÍ×Ôͬ¹¹Èº

Several Properties of Kneser Graph and Its Automorphism Group;

KneserͼµÄÈô¸ÉÐÔÖʼ°Æä×Ôͬ¹¹Èº

No-solvable Block-transitive Automorphism Group of 2-(v,11,1) Designs;

2-(v,11,1)Éè¼ÆµÄ·Ç¿É½âÇø´«µÝ×Ôͬ¹¹Èº

Automorphism and Anti-automorphisms of Quantum Group

Á¿×ÓȺV_q(sl(2))µÄ×Ôͬ¹¹ºÍ·´×Ôͬ¹¹