Group of units U(n) under multiplication modulo n | Modern algebra | group theory |

In this video we will see groups of units under multiplication modulo n. Some of the elements of group of integers under addition modulo n has a multiplicative inverse, these elements are units in ( Z , + n ) . The most beautiful thing is that the set of all these units forms a multiplicative group under multiplication modulo n . We will see all the facts about the group of units in this video.
Link to the basics of the groups :
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#GroupOfUnits #Units #GroupTheory #TheMentorsClasses #Groups

[@p.pmathematics869]

Bhut sandar guruji achhe se samj m a gya thanks 👍

[@Rsingh1]

REALLY AMAZING HAR EK CHEEZ BTAYI HAI AAPNE.....SUPERB.....I didnt. Even thought from where this U(n) originated but this video explained me too much things superbly......every point is worth watching and understanding👍👍👍👍

[@TheMentorsclasses]

It's my pleasure, sir!

[@p.pmathematics869]

You are great sir ji

[@Rsingh1]

O MY GOD....IT WAS DAMN GOOD MZAA A GYA SAMAJHKAR....CRYSTAL CLEAR....VERY VERY WELL DONE👍

[@rameshwarprajapati1983]

Thanks a lot sir... Very nicely explained

[@nitinbansal2564]

Fantastic explanation sir

[@nitishgurjarfitness1025]

Useful video for group theory .. I like it

[@skyfly2325]

Keep going.... excellent way of teaching...

[@TheMentorsclasses]

Thank you 😊

[@RideR-SAM65]

Finally searched the right one.. thanks a lot sir❤️

[@TheMentorsclasses]

Thanks a lot

[@PayalSharma-hb3ef]

Very nice sir🙏

[@shivkumar-fe5kh]

good content

[@rcmathematician8100]

great explanation sir ......thanks

[@TheMentorsclasses]

Thank you sir

[@MuhammadWaseem-md7rd]

👌

[@hritikkumar949]

Nice smile

[@bchandra7743]

Good explanation

[@Saktimayee]

Thank you sir🥰

[@subhamkanu]

Sir The Question was to prove the set of units a group under multiplication modulo n not simple multiplication, you proved it for basic multiplication not multiplication modulo n, sir please look in this matter I have a exam tomorrow and really got confused here

[@mathematicsworld9921]

Well explained 👍👍

[@TheMentorsclasses]

Thank you sir

[@Rsingh1]

Sir Zn mei atleast 2 elements hain jo self inverse hain! But kya same property U(n) pe bhi applicable hai?

[@TheMentorsclasses]

Hmm but U(n) shuld contain more than two elements

[@Rsingh1]

@@TheMentorsclasses thanks a lot

[@Rsingh1]

How do we find generators of U(n) ?

[@TheMentorsclasses]

Firstly U(n) need not be cyclic for every positive integer n. So we can not talk about its generator. In the case U(n) is cyclic for some positive integer n , write the group explicitly and search elements with same order as the group has. These elements will be generators of the group.

[@Rsingh1]

@@TheMentorsclasses clear...
(perfect explaination)

[@AssamCodingVlogging]

Sir 3 has a multiplicative inverse 5 hoga 7 nahi

[@TheMentorsclasses]

Yeah ! It is mistakenly written . I explained that inverse of 3 is 5 but wrote 7 . ( Sorry for the mistake we made )

[@p.pmathematics869]

Sir TGT PGT ki tayari kase kre

[@AssamCodingVlogging]

Sir Group of Unit mein associative property ko proof karna pare toh kaise proof karun .... Please reply

[@TheMentorsclasses]

Simply jaisa multiplication m hota h same krna padega bas sath m ye bhi mention karna padega ki jab bhi product n se jyada hoga to us par multiplication modulo n apply krenge.

[@AssamCodingVlogging]

Ok thank you 😊

[@TheMentorsclasses]

👍 and please subscribe our channel if you didn't yet.

[@knowledgefirst6224]

But sir you don't give any example.Examples are basic foundation for maths.I don't see any example in any of your video on abstract algebra.Only theories are not enough.Please Give at least 5 to 6 examples.

[@TheMentorsclasses]

Sure