Are All Groups Nonempty and How Does the Group Identity Factor In?

  • Context: Undergrad 
  • Thread starter Thread starter blueberryfive
  • Start date Start date
  • Tags Tags
    Groups
Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
1 reply · 2K views
blueberryfive
Messages
36
Reaction score
0
Are all groups nonempty? If so, is it because all groups have an identity (element)?
 
Physics news on Phys.org
Right, the definition of a Group gives us that the group must have a minimum of at least 1 element, the group identity.
 

Similar threads

Undergrad Dfns group action & group, written in terms of the other
  • elias001
  • · Replies 26 ·
  • Linear and Abstract Algebra
Replies
26
Graduate Near-Rings with Noncommutative Addition and Two-Sided Distributivity
  • lpetrich
  • · Replies 4 ·
  • Linear and Abstract Algebra
Replies
4
Undergrad Group like operations that are not associative
  • pervect
  • · Replies 3 ·
  • Linear and Abstract Algebra
Replies
3
Insights Groups, The Path from a Simple Concept to Mysterious Results
  • fresh_42
  • · Replies 17 ·
  • Linear and Abstract Algebra
Replies
17
Undergrad Differences between left vs right actions in some group theory questions
  • elias001
  • · Replies 1 ·
  • Linear and Abstract Algebra
Replies
1
Proving a Subset of a Group is a Group
  • cbarker1
  • · Replies 2 ·
  • Linear and Abstract Algebra
Replies
2
Undergrad Does associativity imply bijectivity in group operations?
  • valenumr
  • · Replies 38 ·
  • Linear and Abstract Algebra
2
Replies
38
Graduate What is the generator of the cyclic group (Z,+)?
  • LagrangeEuler
  • · Replies 7 ·
  • Linear and Abstract Algebra
Replies
7
Undergrad Question about "A Group Epimorphism is Surjective"
  • elias001
  • · Replies 13 ·
  • Linear and Abstract Algebra
Replies
13
Graduate Classification of reductive groups via root datum
  • The Tortoise-Man
  • · Replies 3 ·
  • Linear and Abstract Algebra
Replies
3