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Recent questions tagged group-isomorphism

2 votes

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1

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 1
What is the order of smallest non-cyclic group?

GO Classes asked in Set Theory & Algebra May 29, 2022

344 views

3 votes

1 answer

2

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 10
Let $Z$ be the set of all integers. Let $n \in Z$ and $nZ = {nk : k \in Z}.$ Which of the following is/are true? $nZ$ is a subgroup of $Z$ (under addition operation) for all $n \in Z.$ Every subgroup of ... some $n.$ $3Z$ is the smallest subgroup of $(Z,+)$ containing $3.$ $nZ$ is a cyclic subgroup of $Z.$

GO Classes asked in Set Theory & Algebra May 29, 2022

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2 votes

2 answers

3

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

Sangeethasiva asked in Set Theory & Algebra Sep 27, 2018

by Sangeethasiva

2.0k views

3 votes

1 answer

4

GATE CSE 1987 | Question: 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.

makhdoom ghaya asked in Set Theory & Algebra Nov 15, 2016

by makhdoom ghaya

586 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 $|S| = \infty$

makhdoom ghaya asked in Set Theory & Algebra Dec 19, 2015

by makhdoom ghaya

671 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 $\mathbb{Z}/4$

makhdoom ghaya asked in Set Theory & Algebra Dec 17, 2015

by makhdoom ghaya

297 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 $\mathbb{Z}/4$

makhdoom ghaya asked in Set Theory & Algebra Dec 17, 2015

by makhdoom ghaya

349 views

2 votes

0 answers

8

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

makhdoom ghaya asked in Set Theory & Algebra Dec 9, 2015

by makhdoom ghaya

443 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 $\mathbb{Q}$.

makhdoom ghaya asked in Set Theory & Algebra Dec 9, 2015

by makhdoom ghaya

255 views

2 votes

1 answer

10

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

makhdoom ghaya asked in Set Theory & Algebra Dec 9, 2015

by makhdoom ghaya

463 views

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