[GAP Forum] Minimal Faithful Permutation Representation Degree

[Saad]

Dear all,

 Marston Conder refered to the paper :
MR0390040 (52 #10866)
Wright, D.<https://mathscinet-ams-org.ezproxy.auckland.ac.nz/mathscinet/search/author.html?mrauthid=225357>
Degrees of minimal embeddings for some direct products.
Amer. J. Math.<https://mathscinet-ams-org.ezproxy.auckland.ac.nz/mathscinet/search/journaldoc.html?id=776> 97 <https://mathscinet-ams-org.ezproxy.auckland.ac.nz/mathscinet/search/publications.html?pg1=ISSI&s1=229858> (1975), <https://mathscinet-ams-org.ezproxy.auckland.ac.nz/mathscinet/search/publications.html?pg1=ISSI&s1=229858> no. 4,<https://mathscinet-ams-org.ezproxy.auckland.ac.nz/mathscinet/search/publications.html?pg1=ISSI&s1=229858> 897–903.
20C99<https://mathscinet-ams-org.ezproxy.auckland.ac.nz/mathscinet/search/mscdoc.html?code=20C99>

Which states that the reverse of the inequality holds when the groups G, H have coprime orders

 Alexander Hulpke pointed that it was a bug....its worth to mention that it may not be this case in general considering the orders of the groups, for example:

gap> A:=AlternatingGroup(5);; oA:=Order(A);
60
gap> S:=OneSmallGroup(17,IsSolvable,true);oS:=Order(S);
<pc group of size 17 with 1 generators>
17
gap> D:=DirectProduct(S,A);;
gap> Gcd(oS,oA);
1
gap> muA:=MinimalFaithfulPermutationDegree(A);
5
gap> muS:=MinimalFaithfulPermutationDegree(S);
17
gap> muD:=MinimalFaithfulPermutationDegree(D);
85




Saad Owaid