Ping.
It certainly cleared up some questions I had regarding the commandment to give up one's life rather than violate the three cardinal sins vis a vis Qiddush HaShem Yitbarakh baRabbim (sanctifying G-d's name publicly) requiring a minyan of ten adult male Jews. So one must die rather than commit one of the Three whether or not there is a minyan (which is a requirement only for giving up one's life rather than commit other sins under certain circumstances). Thanks for clearing that up.
If I remember correctly, there is actually a dispute about the requirement of Noachides to sanctify G-d publicly by martyrdom. One opinion is that they are not so required (as the late Rabbi Kaplan here states). A second is that they are required just as Jews to die rather than commit any of the three. And a third is that they are so required only when commanded to commit murder. And I'm sure among those with the latter two opinions there are disagreements about whether or not the requirement applies only in the presence of a Jewish minyan.