Until recently, I believed that a subgroup of a direct product was the direct product of subgroups. Obviously, there exists a trivial counterexample to this statement. I have a question regarding...

May 15, 2012 · A subgroup generated by a set is defined as (from Wikipedia): More generally, if S is a subset of a group G, then , the subgroup generated by S, is the smallest subgroup of G …

Aug 10, 2012 · Subgroup criterion. Ask Question Asked 13 years, 3 months ago Modified 10 years, 4 months ago

Nov 11, 2021 · The question seems very simple, but it's confusing me as the term 'proper subgroup' has different definations in different reference books. I read in galian(7th edition) …

A subgroup is a subset which is also a group of its own, in a way compatible with the original group structure. But not every subset is a subgroup. To be a subgroup you need to contain the …

Mar 15, 2021 · The cyclic subgroup of order $4$ contains an element of order $4$, so the only candidates are $r^3$ and $r$.

Suppose $Q_8$ is isomorphic to subgroup of $S_n$ with $n\leq 7.$ Then it should come from a group action of $Q_8$ on a set of cardinality at most 7. Suppose $Q_8$ acts on a set $A$ with …

Understanding how to prove when a subset is a subgroup Ask Question Asked 9 years, 2 months ago Modified 4 years ago

Oct 25, 2012 · 0 How would you get one, considered that the class equation is $12=1+3+4+4$ and a normal subgroup is union of conjugacy classes?

Mar 7, 2017 · – Cloud JR K Sep 22, 2018 at 7:46 How will apply this result, to determine a subgroup of given order is normal, if the class equation of the group is given – sabeelmsk Dec …