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Hi,

this week i've started to study group theory and there's a thing that i don't understand about cosets: Suppose to have a group ##\textit{G}## and a subgroup ##\textit{H}##, than ##\forall g \in \textit{G}## i can build my left coset ##[g \textit{H}]##. Now, here's my question: Once you have chosen an element ##g_{1} \in \textit{G}##, does my left coset ##[g_{1} \textit{H}]## form a subgroup of ##\textit{G}## or it's just a subset?

Thanks in advance for the help!

this week i've started to study group theory and there's a thing that i don't understand about cosets: Suppose to have a group ##\textit{G}## and a subgroup ##\textit{H}##, than ##\forall g \in \textit{G}## i can build my left coset ##[g \textit{H}]##. Now, here's my question: Once you have chosen an element ##g_{1} \in \textit{G}##, does my left coset ##[g_{1} \textit{H}]## form a subgroup of ##\textit{G}## or it's just a subset?

Thanks in advance for the help!

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