divisors

Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ______.

Let $$G$$ be a finite group on $$84$$ elements. The size of a largest possible proper subgroup of $$G$$ is ________.

The number of divisors of $$2100$$ is ___________.

The number of distinct positive integral factors of 2014 is _______ .

What is the probability that divisor of $${10^{99}}$$ is a multiple of $${10^{96}}$$ ?

(a) If G is a group of even order, then show that there exists an element $$a \ne e$$, the identifier $$g$$, such that $${a^2} = e$$ (b) Consider the set of integers $$\left\{ {1,2...