(adsbygoogle = window.adsbygoogle || []).push({}); Lemma.A group [itex]G[/itex] of order 6 can have only one element of order 3.

Pf.Suppose [itex]G[/itex] has two elements of order 3. Call these elements [itex]x[/itex] and [itex]y[/itex]. Let [itex]H[/itex] and [itex]K[/itex] be the subgroups generated by [itex]x[/itex] and [itex]y[/itex] resp. Then [itex]H \cap K = \{ e \}[/itex] and therefore [itex]G[/itex] can have only one subgroup of order 3.

I'm reading over my notes from class and I'm confused on the reasoning here. Why does [itex]H \cap K = \{ e \}[/itex] imply that [itex]G[/itex] can have only one element of order 3?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question about grp of order 6

Loading...

Similar Threads - Question order | Date |
---|---|

Basic Question: Order of permutations in Sn | Dec 12, 2013 |

Question in Proof of second order condition with linear constraints | Jun 21, 2011 |

Question about order of an element | Dec 1, 2010 |

A question of order of the product of two elements | Mar 25, 2009 |

Question on order of an element | Feb 28, 2009 |

**Physics Forums - The Fusion of Science and Community**