True or False Questions for Chapter 24-33
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For any fixed prime p all Sylow p-subgroups are isomorphic.
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Every group of order p^2 where p is prime is Abelian.
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For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.
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If p^k is a prime-power divisor of the order of a finite group G then G has a subgroup of order p^k.
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If H is a subgroup of a finite group G and H has prime-power order then H is contained in a Sylow subgroup of G.
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If a and b are two group elements of order 2  then the subgroup they generate is dihedral.
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Every  finite plane symmetry group is cyclic or dihedral.
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The composition of a plane rotation and a plane rotation is a plane rotation.
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The composition of a plane reflection and a plane reflection is a plane rotation.
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A crystallographic group cannot have an element of order 5.
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In a crystallographic group it is possible to have a 45 degree rotational symmetry.
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Chap 30 If G is a finite Abelian  group and S is a generating set (nonempty) for G, then Cay(S:G) has a Hamiltonian path.
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Chap 31 A linear code with Hamming weight 5 can correct any received word with two errors and detect any received word with four errors.
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Chap 31 If the Hamming weight of a linear code is 4 then the code can correct any two errors.
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