LEGO Difference Engine

Long before the age of electronic computers, even before Alan Turing invented the theoretical Turing Machine, Charles Babbage invented a mechanical computer which he called the Difference Engine. Andrew Carol rebuilt one using LEGO.


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Problem ( Group Theory )

Show that, then prove.

Let G be a group in which each proper subgroup is contained in a maximal subgroup of finite index in G. If every two maximal subgroups of G are conjugate in G, then G is a cyclic group.