Group Theory (AQA A-Level Further Maths): Flashcards

Groups with same structure via one-to-one mapping

$H \cong G$

$f(p \bullet q) = f(p) \star f(q)$

Element $a$ where $a \bullet a = e$ (identity)

Must correspond to each other

Only ONE structural difference

Different numbers of self-inverse elements

Smallest $n$ where $a^n = e$

Different periods of elements in each group

Group generated by a single element