Suppose G is a group of order 4 and $x^2=e$ for all $x$ in G. Prove that G is isomorphic to $Z_2\oplus Z_2$.
141379
All groups where underlying set has at most 4 elements
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
109286
Galois group of $x^4-2x^2-2$
152741
Cardinal of a group $G$ such that for all $x\in G$ we have $x^2=e$
36137
Prove $GL_2(\mathbb{Z}/2\mathbb{Z})$ is isomorphic to $S_3$
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
36142
What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
37414
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
5297
If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
152603
Group isomorphic to its automorphism group