New posts in Combinatorial Group Theory

Showing $b^2 \notin \langle a \rangle$ for $V_{8n}=\langle a,b:a^{2n}=e, b^4 = e, ba=a^{-1}b^{-1},b^{-1}a=a^{-1}b\rangle.$

Showing $\langle a,p,q\mid p^{-1}ap=a^2, q^{-1}aq=a^2\rangle$ is non-hopfian (from first principles).

Efficient computation of conjugacy classes of a small group.

Does there exist a group that is both a free product and a direct product of nontrivial groups?

Free groups are residually of rank 2

What is the abelianization of $\langle x,y,z\mid x^2=y^2z^2\rangle?$

When is a group isomorphic to the infinite cyclic group?

Homomorphisms of $\mathbb{F}_2$ that preserve $aba^{-1}b^{-1}$

Book Recommendations: Combinatorial Group Theory and Topological Prerequisites.

What is this group $G=\langle a,b,c\mid a^2=1, b^2=1, c^2=ab\rangle$