# Tour:Product of subgroups

From Groupprops

**This article adapts material from the main article:** product of subgroups

This page is part of the Groupprops guided tour for beginners (Jump to beginning of tour)PREVIOUS: Equivalence of definitions of group action|UP: Introduction five (beginners)|NEXT: Permuting subgroups

General instructions for the tour | Pedagogical notes for the tour | Pedagogical notes for this part

WHAT YOU NEED TO DO:

- Read and understand the definition of product of subgroups.
- Try to come up with an explanation for why the product of subgroups need not be a subgroup (i.e., where the proof fails).
- Try to come up with an example in the symmetric group of degree three of a product of subgroups not being a subgroup.

This page is part of the Groupprops guided tour for beginners (Jump to beginning of tour)PREVIOUS: Equivalence of definitions of group action|UP: Introduction five (beginners)|NEXT: Permuting subgroups

General instructions for the tour | Pedagogical notes for the tour | Pedagogical notes for this part