(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] group of order (35)^3

1. The problem statement, all variables and given/known data

Show that every group of order (35)^3 has a normal subgroup of order 125.

2. Relevant equations

3. The attempt at a solution

I was trying to use the Third Sylow Theorem to show that there can only be one Sylow 5-subgroup but 21 Sylow 5-subgroups seems to work fine.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

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

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

# Group of order (35)^3

**Physics Forums | Science Articles, Homework Help, Discussion**