Using Kurosch's subgroup theorem for free proucts,prove that
every finite subgroup of the free product of...
Using Kurosch's subgroup theorem for free proucts,prove that
every finite subgroup of the free product of finite groups is
isomorphic to a subgroup of some free factor.
Prove that every real number with a terminating binary representation (finite number of digits to the right of the binary point) also has a terminating decimal representation (finite number of digits to the right of the decimal point).
Incorrect Theorem. Let H be a finite set of n horses. Suppose
that, for every subset S ⊂ H with |S| < n, the horses in S are
all the same color. Then every horse in H is the same color.
i) Prove the theorem assuming n ≥ 3.
ii) Why aren’t all horses the same color? That is, why doesn’t
your proof work for n = 2?
. Let Π be a finite incidence geometry. Prove that, if every
line in Π has exactly n points and every point in Π lies on exactly
n + 1 lines, then Π is an affine plane. Come up with a similar
criterion for finite geometries satisfying (EP) (those geometries
are called projective planes).