The Mathieu group M24 as we knew it -- The amalgam method -- L4(2) in two incarnations and L3(4) -- From L5(2) to the Mathieu amalgam -- M24 as universal completion -- Maximal subgroups -- The 45-representation of M24 -- The held group -- The inevitability of Mathieu groups -- Locally projective graphs and amalgams.
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The Mathieu Groups are presented in the context of finite geometry and the theory of group amalgams.