Recent content by lmn123

Homework Statement For each m >= 2, find a group with a composition series of length 1 with a subgroup of length m. Homework Equations Simple groups iff length 1. If G is abelian of order p1^k1...pr^kr, then length G = k1 + ... + kr If G has a composition series and K is normal...

Suppose for a second that I did not need to worry about half open intervals is my above proof right then? Now suppose I do need it in a more general case. What about this. Given any interval besides the trivial case [x,x], there exits two points, y and z, within the interval such that y <...

Homework Statement If the domain of a continuous function is an interval, show that the image is an interval. Homework Equations Theorem from book: f is a cont. function with compact domain D, then f is bounded and there exists points y and z such that f(y) = sup{ f(x) | x ∈ D} and...