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 neutral …

Mar 25, 2026 · Explore related questions group-theory finite-groups nilpotent-groups frattini-subgroup See similar questions with these tags.

Understanding how to prove when a subset is a subgroup Ask Question Asked 9 years, 7 months ago Modified 4 years, 5 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) that the subgroup of G …

Mar 21, 2018 · To summarise: in the first case the circle is a subgroup and the index is infinite with one coset corresponding to every possible positive number as radius. In the second case positive real …

A subgroup of order 3 is isomorphic to $\Bbb Z_3$, so it is generated by an element of order 3. To identify the subgroups of order 3 it suffices to identify the elements of order 3.

Mar 1, 2026 · Then the Klein 4-group is the subgroup whose non-identity elements are the rotations about the three mutually perpendicular lines that join midpoints of pairs of opposite edges. You can …

Dec 22, 2024 · When is the stabilizer a normal subgroup? Ask Question Asked 1 year, 3 months ago Modified 1 year, 3 months ago

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 containing …

Edit: Written this assuming you've taken a course on group theory. Finding all subgroups of large finite groups is in general a very difficult problem. Usually, I'd start with Lagrange's theorem to find …