Michael Anshel

2004-08-09 14:40:10 UTC

In P.J.Cameron's, Permutation Groups, LMS 45 CUP (1999) p. 49 the following

problems is posed:

Problems:

(1) What does the Parker Vector of a permutation group G tell us about G.

(2) In particular,which groups or classes of groups are determined by P(G)?

Generally what progress has been made on problems ? In R.A. Parker's

paper "The Computer Calculation of Modular Characters" In Computational Group

Theory ,ed M.D. Atkinson Academic Press (1984) p.272

Parker remarks that if A1 ,B1, generate a representation and A2 ,B2 generate

another of the same dimensions then using the methods described in his

paperthat a simultaneous solution to the equations

X A1 X^(-1)= A2, X B1X^(-1)X

can be computed should one such solution exist.

This same equations arose in another context AAG 1999

I. Anshel,M. Anshel and D. Goldfeld, "An Algebraic Method for

Public-Key Cryptography Mathematical Research Letters 6,1-5,(1999)

and interested readers are invited to contact me regarding AAG 1999.

This researcher would like to thank Professor Alex Ryba for introducing

Parker's ideas and methods in a recent conversation.

Professor Michael Anshel

Department of Computer Sciences R8/206

The City College of New York

New York,New York 10031

http://www-cs.engr.ccny.cuny.edu/~csmma/

***@cs.ccny.cuny.edu

***@aol.com

problems is posed:

Problems:

(1) What does the Parker Vector of a permutation group G tell us about G.

(2) In particular,which groups or classes of groups are determined by P(G)?

Generally what progress has been made on problems ? In R.A. Parker's

paper "The Computer Calculation of Modular Characters" In Computational Group

Theory ,ed M.D. Atkinson Academic Press (1984) p.272

Parker remarks that if A1 ,B1, generate a representation and A2 ,B2 generate

another of the same dimensions then using the methods described in his

paperthat a simultaneous solution to the equations

X A1 X^(-1)= A2, X B1X^(-1)X

can be computed should one such solution exist.

This same equations arose in another context AAG 1999

I. Anshel,M. Anshel and D. Goldfeld, "An Algebraic Method for

Public-Key Cryptography Mathematical Research Letters 6,1-5,(1999)

and interested readers are invited to contact me regarding AAG 1999.

This researcher would like to thank Professor Alex Ryba for introducing

Parker's ideas and methods in a recent conversation.

Professor Michael Anshel

Department of Computer Sciences R8/206

The City College of New York

New York,New York 10031

http://www-cs.engr.ccny.cuny.edu/~csmma/

***@cs.ccny.cuny.edu

***@aol.com