Recent questions in Abstract algebra

Judith McQueen
2022-01-15
Answered

\(\displaystyle{S}={\frac{{{R}}}{{-{1}}}}\) and define a binary operation on S by \(\displaystyle{a}\times{b}={a}+{b}+{a}{b}\). Prove that \(\displaystyle{\left({S},\times\right)}\) is an abelian group.

Lennie Davis
2022-01-15
Answered

\(\displaystyle{f}:{\left({\mathbb{{{Z}}}}_{{{28}}},+\right)}\rightarrow{\left({\mathbb{{{Z}}}}_{{{16}}},+\right)}\)

be a group homomorphism such that \(\displaystyle{f{{\left({1}\right)}}}={12}\)

Find \(\displaystyle{k}{e}{r}{\left({f}\right)}\)

Jason Yuhas
2022-01-15
Answered

Sallie Banks
2022-01-15
Answered

Let G be any group and N be a subgroup.

\(\displaystyle{\left({a}{N}\right)}{\left({b}{N}\right)}={a}{b}{N}\)

Maria Huey
2022-01-15
Answered

Group structure of given \(\displaystyle{2}\times{2}\) matrix group over \(\displaystyle{\mathbb{{{F}}}}_{{{3}}}\)

Nicontio1
2022-01-14
Answered

Determine

\(K\triangleleft G,\ \frac{G}{K}\simeq H_{1}\)

and

\(\displaystyle{K}\stackrel{\sim}{=}{H}_{{{2}}}\)

osteoblogda
2022-01-14
Answered

Deragz
2022-01-14
Answered

lunnatican4
2022-01-14
Answered

Arthur Pratt
2022-01-14
Answered

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