Recent content by rourky

[b]1. I am just looking for a defn, I can't find it on the net: Given a ring R, a, b elements of R, (a?) gcd(a,b) is defined to be? [b]3. I am guessing that if d/a and d/b and for any other e such that e/a and e/b we have e/d, then d is (a?) gcd of a and b. Is this correct, and is...

Thanks Matt, A little "over my head". Not your fault though, just haven't heard of the terms "transitive subgroup" and "transitive group action". Unfamiliar with opening result as well, actually thought it was Cayley's theorem at first. Really appreciate the help, now happy in the...

[b]1. G a Group of order 60, G simple, prove G isomorphic to A5 [b]2. Familiar with Sylow's Theorems, theorems leading up to Sylow. [b]3. We make the assumption that G is not isomorphic to A5 Then "given G cannot have a subgroup of index 2, 3, 4, 5," I can get...

Thanks Dick, that's the second time you've helped me out this week.

Homework Statement Defn: A subset A of a metric space (X, d) is NOWHERE DENSE if its closure has empty interior. Now I am told that this implies 1. A is nowhere dense iff closure of A does not contain any non-empty open set and 2. A is nowhere dense iff each non-empty open set has a...

Thanks for your replies guys, problem solved! Yes, I was assuming a topology by a metric, sorry for not stating so.

Homework Statement Question: Prove Int(A) is an open set, given Int(A) is the set of all interior pts of A where x is an interior pt of A if it is the centre of an open ball in A. Homework Equations None The Attempt at a Solution Attempted Soln: Suppose x is an element of...