Answer Abstract Algebra Questions - LCM & Subgroups

In summary, the conversation involves someone seeking answers for two questions related to additive groups and subgroups in mathematics. The first question is about showing that nZ intersection mZ= lZ, where l is the least common multiple of m and n. The second question involves proving that (H union K) is a subgroup of G if and only if H is a subset of K or K is a subset of H. The requester also expresses urgency for the answers, but is advised to post in the appropriate forums for help and to put in effort as this is not a place to get homework done.
  • #1
uob_student
22
0
hello

i have two questions and i need answers for them

first one:

in the additive group (Z,+)
show that nZ intersection mZ= lZ

, where l is the least common multiple of m and n.



The second question is :

Given H and K two subgroups of a group G , show the following:

(H union K) subgroup of G if and only if H subset of K or K subset of H

:confused:

:smile:
 
Physics news on Phys.org
  • #2
i need the answers quickly
 
  • #3
Post them in the correct place and you might get some answers. Try the homework forum, or the maths forum, not this one.

Plus, saying things like 'i need the answers quickly' indicates this is for a homework assignment. You won't just be given the answers, this isn't a place where you get your homework done, so bear that in mind,
 

What is the LCM (least common multiple) in abstract algebra?

The LCM in abstract algebra refers to the smallest positive integer that is divisible by both of the given numbers. In other words, it is the smallest number that is a multiple of both numbers. This concept is often used in abstract algebra to find the least common multiple of polynomials or other algebraic expressions.

How do you find the LCM of two or more numbers in abstract algebra?

To find the LCM of two or more numbers in abstract algebra, you can use the prime factorization method. First, factor each number into its prime factors. Then, identify the common factors and the highest power of each common factor. Finally, multiply the common factors by the highest power to get the LCM.

What are subgroups in abstract algebra?

In abstract algebra, subgroups are subsets of a group that also form a group under the same group operation. In other words, a subgroup is a smaller group within a larger group. They have the same properties as the larger group, but with a smaller set of elements.

What is the significance of subgroups in abstract algebra?

Subgroups play a crucial role in abstract algebra as they allow us to break down a larger group into smaller, more manageable groups. This can help us understand the structure of a group better and make it easier to solve complex problems. Additionally, subgroups have many applications in other areas of mathematics such as number theory and geometry.

How do you determine if a subset is a subgroup in abstract algebra?

To determine if a subset is a subgroup in abstract algebra, you need to check if it satisfies the three conditions for a subgroup: closure, associativity, and inverses. This means that the subset must be closed under the same operation as the larger group, the operation must be associative, and every element in the subset must have an inverse within the subset. If these conditions are met, the subset is a subgroup of the larger group.

Similar threads

  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
3K
  • Calculus and Beyond Homework Help
Replies
1
Views
987
  • Calculus and Beyond Homework Help
Replies
4
Views
781
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
2K
  • Linear and Abstract Algebra
Replies
1
Views
643
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
Back
Top