Why is the smallest subgroup of G containing A and B equal to G itself?

  • Level: Graduate 
  • Thread starter Thread starter blahblah8724
  • Start date Start date
  • Tags Tags
    Example Group Subgroup
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
1 reply · 3K views
blahblah8724
Messages
31
Reaction score
0
In an example it says that, if [itex]|G| = 15[/itex] and [itex]G[/itex] has subgroups [itex]A,B[/itex] of [itex]G[/itex] with [itex]|A| = 5[/itex] and [itex]|B| = 3[/itex], then [itex]A \cap B[/itex] must equal [itex]\{e_G\}[/itex] and the smallest subgroup of [itex]G[/itex] containing both [itex]A[/itex] and [itex]B[/itex] is [itex]G[/itex] itself. Could anyone explain why? Thanks!
 
Physics news on Phys.org