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 _______________________________________________ Forum mailing list [email protected] https://mail.gap-system.org/mailman/listinfo/forum
