Dear forum, sorry, I may be confused by "reverse inequality" which proved clearly in :
Minimal Permutation Representations of Finite Groups Author(s): D. L. Johnson Source: American Journal of Mathematics, Vol. 93, No. 4 (Oct. 1971), pp. 857-866 to be : $\mu(G\times H)\leq \mu G +\mu H $ ( for any finite groups G, H) $\mu(G\times H)\geq \mu G +\mu H $ ( for groups G, H of coprime orders) hence, $\mu(G\times H)= \mu G +\mu H $ ( for any finite group of coprime orders) and equality is the ultimate value for any finite groups, Saad Owaid. On Sunday, September 1, 2019, 11:15:11 PM GMT+3, Saad <saadhal...@hotmail.com> wrote: 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 Forum@gap-system.org<mailto:Forum@gap-system.org> https://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
