Question: Let p be a prime and let G be a group of order p 2 . Prove that G contains an element of order p

Let p be a prime and let G be a group of order p2 .

Prove that G contains an element of order p .

Is it true that G must also contain an element of order p2 ?

Justify your answer by giving either a counter-example or a proof.

Please use latex as hand written images are difficult to interpret.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

(a) The curve y=x+3x+4 is translated by Find and simplify the equation of the translated curve. [2]

Q:

Use proposition 13: |PN|= |P||N| / |P intersect N| isomorphism theorem 7. Let p be a prime and let G be a group of order pom, where p does not divide m. Let P be a subgroup of G of order pa and let N...

Q:

Math 411 Homework Assignment 7 Due 3/24/2017 by the end of lecture 1. (a) Show that the cycle (a1 a2 . . . ak ) Sn is even if and only if k is odd. (b) Suppose = (a1 a2 ) is a transposition and let...

Q:

answer all parts please 2. Let G = SL(2, Z), let p be a prime number, and consider the set U of 2 x 2 integer matrices whose determinant is p. Then G acts on U by left multiplication, i.e. if o E G,...

Q:

(4) (a) (9 points) Suppose that a group G of order p, which is a prime num- ber, acts on a set X. Prove that for every x E X we have either StabG(x) = {e} or Staba(x) = G. (b) (9 points) Let p > 2 be...

Q:

(4) (a) (9 points) Suppose that a group G of order p, which is a prime num- ber, acts on a set X. Prove that for every x E X we have either StabG(x) = {e} or Staba(x) = G. (b) (9 points) Let p > 2 be...

Q:

Let p be a prime, (a) If G has order 2p, prove that every proper subgroup of G is cyclic, (b) If G has order p2, prove that G has a subgroup of order p.

Q:

Let G be a group of order 2 n ; then G contains an element of order 2. If n is odd and G abelian, there is only one element of order 2.

Q:

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Q:

Kindly 51. 52. 53. 54. 55. 56. 57. 58. 59. 1 - .- - _J_'___'_'__J is a subgroup of Z Suppose that G is a nite group with the property that every non- identity element has prime order (for example,...

Q:

please typ.e this answer on page BY HANDWRITING TO LOOK CLEAR question solution (a) Let G be a group of order p, which is a prime number, acting on a set X. Then for every X we have either Stabc(x)=...

Q:

You are to enter the following items in the books of eriginal entry, post to personal accounts, und show the transfer to the general ledger. 1 Cedit purchases (in Esi from 390 560 K.Hill M. Nueman N....

Q:

Why are these two sums equal? Why are the two added on the right, why is there a floor function as the upper bound of the right sum, and why does this allow for us to get rid of the absolute value? ...

Q:

The finance department at Lumos Corporation is analyzing what took place during Q 1 since the actual performance was significantly lower than expected. What type of analysis is the finance department...

Q:

please send full answer In early December Alice and Bob decided to open Sample Cafe with $14,000 of their own money and $20,000 borrowed from a friend. They have spent $13,000 on equipment and...