论文信息 - Automorphism groups of 2-groups

Automorphism groups of 2-groups

Abstract A well-known conjecture on p-groups states that every non-abelian p-group G has the property that | G | divides | Aut ( G ) | . We exhibit periodic patterns in the automorphism group orders of the 2-groups of fixed coclass and we use this to show that for every positive integer r there are at most finitely many counterexamples to the conjecture among the 2-groups of coclass r.

Bettina Eick

[1] Bettina Eick,et al. Determination of the Uniserial Space Groups with a given Coclass , 2005 .

[2] R. M. Davitt,et al. On the Automorphism Group of a Finite p-Group with a Small Central Quotient , 1980, Canadian Journal of Mathematics.

[3] W. Gaschütz. Nichtabelsche p-Gruppen besitzen äussere p-Automorphismen , 1966 .

[4] Bettina Eick,et al. CONSTRUCTING AUTOMORPHISM GROUPS OF p-GROUPS , 2002 .

[5] D.J.S. Robinson. Groups – St Andrews 1981: Applications of cohomology to the theory of groups , 1982 .

[6] Avinoam Mann,et al. Some questions about p-groups , 1999, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[7] C. R. Leedham-Green,et al. The Structure of Groups of Prime Power Order , 2002 .

[8] E. A. O'Brien,et al. The p-Group Generation Algorithm , 1990, J. Symb. Comput..

[9] Eamonn A. O'Brien,et al. CLASSIFYING 2-GROUPS BY COCLASS , 1999 .

[10] Albert D. Otto. Central automorphisms of a finite$p$-group , 1966 .

[11] M. F. Newman,et al. Space groups and groups of prime-power order I , 1980 .

[12] Kenneth S. Brown,et al. Cohomology of Groups , 1982 .