Let be a subgroup of order 2 in . Show that . Deduce that if , then .
Say .
We already know that . Now suppose ; then . Clearly, then, we have . Thus . Hence .
If , we have . Then for all , so that for all , and thus .
Let be a subgroup of order 2 in . Show that . Deduce that if , then .
Say .
We already know that . Now suppose ; then . Clearly, then, we have . Thus . Hence .
If , we have . Then for all , so that for all , and thus .
On these pages you will find a slowly growing (and poorly organized) list of proofs and examples in abstract algebra.
No doubt these pages are riddled with typos and errors in logic, and in many cases alternate strategies abound. When you find an error, or if anything is unclear, let me know and I will fix it.
Comments
In the last sentence, should be .
Thanks!