A group is an algebraic structure consisting of a set of elements together with an operation that satisfies four conditions: closure, associativity, identity and invertibility. Group theory studies groups.

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Structure of the group $\{1+p\mathbb Z_p \}$

In preparation for algebraic number theory I am reading Serre : A course in Arithmetic. I stuck in understanding a proof (p.17): Notation: $U_n=1+p^n\mathbb Z_p$ Actually there are many things ...