Abstract Algebra: Non-Cyclic Group of Order 10 | Orders and Subgroups

Описание: #cyclicsubgroups #cyclicgroup #grouptheoryWelcome to Maths Mastery with Dr Upasana P Taneja.

I’m Dr Upasana Taneja, and on this channel, I teach higher-level mathematics including Algebra, Group Theory, Ring Theory, Real Analysis, and Complex Analysis for BSc, MSc, NET, GATE, and IIT-JAM students.

In this 5-minute video, we’ll discuss the construction of a non-cyclic group of order 10 and explore its structure and properties.
You’ll learn:

How to construct a non-cyclic group of order 10

Why this group is not cyclic

The order of each element in the group

The number and order of subgroups

How this group is isomorphic to D₅ (the dihedral group of order 10)


This concise explanation will help you clearly understand the difference between cyclic and non-cyclic groups, and build a strong foundation in Group Theory — essential for BSc, MSc, NET, GATE, and IIT-JAM Mathematics.

For detailed notes and examples, visit my blog: [email protected]

#MathsMastery #DrUpasanaTaneja #NonCyclicGroup #GroupTheory #DihedralGroup #AbstractAlgebra #OrderOfElements #Subgroups #HigherMaths #BScMaths #MScMaths #NETMaths #GATEMaths #IITJAMMaths #MathConcepts #LearnMathsOnline #ShortMathsVideo #MathLecture #MathEducation