Every subgroup of a cyclic group is cyclic.

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Sir book m lengthy tha boht apne easy way m smjha diya ♥️

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Are aap yha bhi

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Me to ratunga ise, kuch smjh nai aa rha

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Found this after being disappointed by gazendra purohit sir ❤‍🩹

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Thank you sir excellent 👍❤

[@Renu-us6fs]

Excellent sir

[@Subho_0513]

Dua koro sir
Mera paper thik se jaye

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Well explained Sir!!

[@Yeahmansingh]

thanks you made it very easy to understand

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Very hardworking sir 👨‍🏫

[@Rahul12345-p]

Thank you dada,khub help holo

[@Subho_0513]

Sir kal mera group theory ka exam he .

[@user-yr9dy7oj1p]

Sir .. kindly guide me to answer the below question. Let G be a finite group. Then show that o(G) = o(Z(G)) + ∑[G:N(a)]>1[G : N[a]]

[@rutujapande2020]

Thank you sir

[@Renu-us6fs]

Sir pdf iss chapter k chaiye

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Thanku . Nd ur writing too good sir ...

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Thank you

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New Subscriber Sir ☺️

[@MathsICU]

Thanks for subbing!

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Itna lambaa

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Good

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good

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Love From Purulia (west bengal)

[@MathsICU]

Best wishes 👍

[@Subho_0513]

@@MathsICU thank you Sir

[@sm-qh2zp]

H =({i^-³, i², i³,i⁴},×)
Here in i²,i³,i⁴→2,3,4 are positive so take it as it is
In i-³ → -3 is negative taki inverse of i-³ i.e. i³.
Now the obtained element ao far is in some positive power of i and belongs to H (i.e. {i³,i²,i³,i⁴} but are not forming group

[@sanamsanam7529]

Sir is theorem ka hum use kaha per karta hai

[@MathsICU]

For example Z5 is a cyclic group with respect to addition modulo 5
Therefore every subgroup of Z5 is also cyclic
You do not need to check their cyclicness.

[@birupakshchoudhury7057]

lovely proof

[@inzanevlog1816]

your handpen 😧

[@mathematics9334]

Sir ,
b€H and a^k€H
=> b.( a^k)€H. (By closure property)
How can we say that
b.( a^k) ^(-q)€H.

[@MathsICU]

We know that if a belongs to H (a€ H) then every integral power of a is also in H. (a^k€ H for every k in the set of integers) , H being a subgroup.
Thus a^k € H then every integral power of a^k is also in H.
(a^k)^(-q) € H

[@mathematics9334]

@@MathsICU Ok sir , now I got it.
Thank you so much . Now it is clear.

[@varunchoudhary8149]

.

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Thank you sir

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Thank you sir