Semi-Direct Products
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Revision as of 23:35, 7 December 2022 by Kfagerstrom (talk | contribs)
Let \(H \) and \( K\) be groups and let \(\rho:K\to \text{Aut}(H) \) be a homomorphism. The (external) semidirect product induced by \(\rho \) is the set \(H\times K \) with the binary operation defined by \((h,k)(h',k')=(h\rho(k)(h') ,kk')\). This group is denoted by \( H \rtimes_p K\)
