Comments by "" (@zachrodan7543) on "Why Do Sporadic Groups Exist?" video.

  1. This may be a silly question, posed by someone who is not yet at the level of math education where i have the ability to start studying group theory (i'm working on it: i am taking the prerequisite class to apply for declaring a math major this fall), but given that M24 contains M23, just by fixing an element in place; and M23 contains M22 likewise, and M22 contains a lee group by the same logic (and presumably the pattern continues downwards), how do we know for certain that M24 isn't a subgroup of some other group going the other direction, which could then have more transitivity? Or do we know for certain that this hypothetical "M25" doesn't exist?
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