Question

Prove or disprove: The group Q∗ is cyclic.

Answer #1

Prove or disprove the following statement. If the statement is
false give a counterexample:
The automorphism group of a finite cyclic group is always
cyclic.
Thank you.

Prove or disprove that [(p → q) ∧ (p → r)] and [p→ (q ∧ r)] are
logically equivalent.

Prove that the property that a group is cyclic is a structural
property.

Suppose that G is a cyclic group, with generator a. Prove that
if H is a
subgroup of G then H is cyclic.

prove that if G is a cyclic group of order n, then for
all a in G, a^n=e.

Can there be an element of infinite order in a finite group?
Prove or disprove.

(a) Prove or disprove: Let H and K be two normal subgroups of a
group G. Then the subgroup H ∩ K is normal in G. (b) Prove or
disprove: D4 is normal in S4.

If n is a square-free integer, prove that an abelian group of
order n is cyclic.

Let G be a group of order 4. Prove that either G is cyclic or it
is isomorphic to the Klein 4-group V4 =
{1,(12)(34),(13)(24),(14)(23)}.

[Q] Prove or disprove:
a)every subset of an uncountable set is countable.
b)every subset of a countable set is countable.
c)every superset of a countable set is countable.

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