Recent questions tagged group-isomorphism

0 votes

1 answer

1

ISI-MMA-2015-92
Consider the group $G \;=\; \begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{-1} \end{pmatrix}\;: a,b \in \mathbb{R},a>0 \end{Bmatrix}$ ... order (D) $N$ is a normal subgroup and the quotient group is isomorphic to $\mathbb{R}^{+}$(the group of positive reals with multiplication).

asked Mar 6, 2019 in Set Theory & Algebra by ankitgupta.1729 Boss (17.1k points) | 140 views

0 votes

1 answer

2

Non isomorphic group of order 10
Number of non isomorphic group of order 10

asked Sep 27, 2018 in Set Theory & Algebra by Sangeethasiva (5 points) | 301 views

+2 votes

1 answer

3

GATE1987-9f
Give the composition tables (Cayley Tables) of the two non isomorphic groups of order 4 with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.

asked Nov 15, 2016 in Set Theory & Algebra by makhdoom ghaya Boss (30.8k points) | 217 views

+1 vote

1 answer

4

UGCNET-June2014-II-21
Consider the graph given below as : Which one of the following graph is isomorphic to the above graph ?

asked Jun 27, 2016 in Graph Theory by makhdoom ghaya Boss (30.8k points) | 1.2k views

+2 votes

1 answer

5

TIFR-2015-Maths-A-4
Let $S$ be the collection of (isomorphism classes of) groups $G$ which have the property that every element of $G$ commutes only with the identity element and itself. Then $|S| = 1$ $|S| = 2$ $|S| \geq 3$ and is finite. $|S| = \infty$

asked Dec 19, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (30.8k points) | 88 views

+1 vote

0 answers

6

TIFR-2014-Maths-B-5
Which of the following groups are isomorphic? $\mathbb{R}$ and $C$ $\mathbb{R}^{*}$ and $C^{*}$ $S_{3}\times \mathbb{Z}/4$ and $S_{4}$ $\mathbb{Z}/2\times \mathbb{Z}/2$ and $\mathbb{Z}/4$

asked Dec 17, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (30.8k points) | 83 views

+1 vote

0 answers

7

TIFR-2014-Maths-B-3
Let $S_{n}$ be the symmetric group of $n$ letters. There exists an onto group homomorphism From $S_{5}$ to $S_{4}$ From $S_{4}$ to $S_{2}$ From $S_{5}$ to $\mathbb{Z}/5$ From $S_{4}$ to $\mathbb{Z}/4$

asked Dec 17, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (30.8k points) | 74 views

+1 vote

0 answers

8

TIFR-2011-Maths-B-7
There is a non-trivial group homomorphism from $S_{3}$ to $\mathbb{Z}/3\mathbb{Z}$.

asked Dec 9, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (30.8k points) | 179 views

+1 vote

0 answers

9

TIFR-2011-Maths-B-3
There are n homomorphisms from the group $\mathbb{Z}/n\mathbb{Z}$ to the additive group of rationals $\mathbb{Q}$.

asked Dec 9, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (30.8k points) | 97 views

+1 vote

1 answer

10

TIFR-2011-Maths-A-22
There exists a group with a proper subgroup isomorphic to itself.

asked Dec 9, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (30.8k points) | 149 views

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