Group Theory 6, order of a Group, order of an element

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Group Theory, order of a Group, order of an element

LadislauFernandes

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Really enjoying the series so far. Just wanted to let you know that this video appears out of order in your "Group Theory" playlist. I'm guessing it was not intentional because the next video (7) introduces subgroups.

koozdra

11^2 (mod15) right? since you are in U(15)... so just get 121 and subtract 15 till you get inside U(15)... you will do this 8 times
or, 121 - 15 x 8 = 1
tks for watching the videos

LadislauFernandes

i know its a stupid question but, how can i find U(n) i m not getting it

smstheaz

Your videos are very helpful. Your explanations are clear and understanding. Thank you very much!

liltv

With the order of a group, is it the number of distinct elements or is it just the number of elements?

ib

yes, since 11 and 14 are relativity prime, this means that there is no number which divide both 11 and 14 except 1.

fawzyhegab

small mistake
8:38 16 modulo 15 should be 1
But i understand you meant to say the order of 4 is 2.
Great video. So much better than reading an arcane textbook.

xoppa

I am giving you a link in the video description ok?
Its just the elements of Z_n "relatively prime" to n.
Or the "units" of Z_n
Imagine you have Z_14 = {0, 1, 2, ...13} right? But now you will take only the elements relatively prime to 14, so that will be:
U(14)={1, 3, 5, 9, 13}
Not the "prime numbers", e.g., check that 7 is not there.
I will make a video for that... you are not the first person asking that...

LadislauFernandes

what do the elements of U(10) come from. why are those elements 1, 3, 7, 9? Thanks

YaWePcGame

your videos are really great.please make videos on metric spaces and topology covering proofs as well as practice problems .thanks in advance
regards

Money__Matters

thank you... modern mathematics made easy...feeling relaxed..

cscor

dear sir in your video you write u(10)={1, 3, 5, 7, 9} what does it called and how this set becomes kindly reply

mansoorakhtar

I am looking for tutor.. Is there anyone who can help me for abstract algebra or other math subjects

mzfhhyx

Great sir how to find number of subgroup of order 2 of a group of order12

albron

IB students that sutdy from here for the exams os n14 had the first question all correct

emprendeperez

So, why don't you actually explain how 7^1=7, 7^2=4, etc... wtf... Why I am so fucking stupid?

chunkylover

Thanks for your video!
Just want to add a correction to the order of 4 at 8:30
16 modulo 15 is 1. so |4| = 1, and not 2

CallMeMantou

am really enjoying the lesson thank you

owusualfredkwabena

Notes lo vunna vidham ga chepparu but explanation correct ga evvale
Sorry to say this

renupanthangi

i think i have to follow joseph gallian contemporary abstract algebra

Maths_Magic_

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