An INSPIRE scholar, post graduate from University of Delhi, enthusiastic and disciplined person

Harpinder Singh

The course describes various properties and theorems on cyclic groups under the main topic Group Theory.

Crack UPSC CSE Prelims and Mains Exams. Know how to prepare for UPSC 2019 and 2020, complete syllabus, exam patterns, latest notifications to join IAS, IFS, IPS and other cadres of Civil Services.

UPSC CSE - GS

UPSC - Civil Services Examination (IAS) Preparation

English

Group Theory: Cyclic Groups

Mathematics

Practice & Crash Course

Environment & Ecology

UPSC CSE

Ace the toughest competitive and government exams in India 

Test Preparation

Union Public Service Commission Exams (UPSC)

Cyclic Groups: Introduction

Theorem on number of generators in an infinite cyclic group.

Theorem 1

Theorem 2

Number of generators in finite cyclic group

Theorem 3

Subgroups of Cyclic Groups

Proof of two theorems on subgroups of cyclic groups.

Theorems on Subgroups of Cyclic Groups

Summary of the theorems on the subgroups of the cyclic groups

Summary

Theorem 4: Subgroups

Questions - 1

Questions based on cyclic groups and their subgroups

Questions - 2

Questions - 3

[Rachna Shukla] PSIR Optional Faculty, Computer science Engineer, Use code : "ASHNASISODIA" to unlock classes.

Ashna Sisodia

In this course, the educator will analyse the important facts and concepts that can be asked in environment section of GS 3 paper in mains examination as well as for Preliminary examination of UPSC CSE.

Enviornment (GS 3) Most Probable Topics for UPSC CSE 2018 - Pre and Mains

India's Top Geography Educator | Use invite code - 'SGYT10' to Unlock my Free Content | Explore the World of Geography like a Pro!

Sudarshan Gurjar

This Course is about Highly yielding topics related with Current Government programs in Environment. Highly recommended for UPSC, State, PSC

(Hindi) Government Programmes and Schemes - Environment for UPSC

Travelling gives you 'experience' & teaching 'immortalizes' it.  Loves both :)  

Vimal Singh Rathore

In this course, aspirants will get to know all the important concepts, conventions, agreements and latest initiatives in Environment and Ecology, for UPSC/IAS and all other competitive exams.

(Hindi) Everything in Environment and Ecology for UPSC/IAS

In this course Vimal has explained all the important conventions on Environment and Ecology. This is one of the most important and scoring section of UPSC Prelims and other State Civil Services Exams.

Important International Conventions on Environment and Ecology

Everything in Environment and Ecology for UPSC/IAS

This Course is All about Eutrophication!! This Course is beneficial for UPSC CSE aspirants.

Lessons

11 lessons • 1h 36m

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Cyclic Groups: Introduction

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Theorem 1

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Theorem 2

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Theorem 3

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Subgroups of Cyclic Groups

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Theorems on Subgroups of Cyclic Groups

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Summary

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Theorem 4: Subgroups

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Questions - 1

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Questions - 2

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