Recent questions tagged tifrmaths2018

True/False Question :Let $G$ be a finite group with a normal subgroup $H$ such that $G/H$ has order $7$. Then $G\cong H\times G/H$.

True/False Question :The multiplicative group $\mathbb{F}_{7}^{\times }$ is isomorphic to a subgroup of the multiplicative group $\mathbb{F}_{31}^{\times }$.

True/False Question :A countable group can have only countably many distinct subgroups.

True/False Question :There exists a continuous surjection from $\mathbb{R}^{3}-S^{2}$ to $\mathbb{R}^{2}-\left \{ \left ( 0,0 \right ) \right \}$ (here $S^{2}\subset \mat...

True/False Question :The permutation group $S_{10}$ has an element of order $30$.

True/False Question :Let $G$ be a finite group and $g \in G$ an element of even order. Then we can colour the elements of $G$ with two colours in such a way that $x$ and...