Prove that infinite group must have an infinite number of subgroups.
96614
Finite number of subgroups $\Rightarrow$  finite group
122821
Is the following proof valid? About the closure of a subgroup, of a topological group, being again a subgroup
87766
Using Cayley's Theorem to find an isomorphic subgroup.
96910
Prove the following alternative group definition.
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
58688
Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite
14301
Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
6189
Examples of infinite groups such that all their respective elements are of finite order.
139078
Infinite partition of $\mathbb N$ by infinite subsets
136167
Prove that structure $(Q/{0}; =;*)$ has infinite number of automorphisms
9232
Group with proper subgroups infinite cyclic
92057
Prove that for every odd integer n, there is a group...
106660
Every subgroup of the integers has finite index
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
128692
Example of an infinite group where every element except identity has order 2
33387
Proof that $n\Bbb Z \leq \Bbb Z$ and are the only subgroups of $\Bbb Z$