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2022-05-20T03:49:59+00:00
Cardinality of underlying set of a profinite group need not determine order as a profinite group
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Conjecture that most finite groups are nilpotent
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Degree of irreducible representation divides order of group
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4
Exponent divides order in finite group
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Exponent of a finite group has precisely the same prime factors as order
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2
Finitely many subgroups iff finite
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Lagrange's theorem
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2
Minimal normal subgroup with order greater than index is characteristic
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Minimal normal subgroup with order not dividing index is characteristic
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Order of a profinite group need not determine order as a group in the sense of cardinality of underlying set
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Order of direct product is product of orders
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0
Order of element divides order of group
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Order of extension group is product of order of normal subgroup and quotient group
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Order of quotient group divides order of group
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Order of semidirect product is product of orders
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1
Pyber's theorem on logarithmic quotient of number of nilpotent groups to number of groups approaching unity
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Size of conjugacy class divides order of inner automorphism group
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Square of Schur index of irreducible character in characteristic zero divides order
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