Ads
related to: lattice of subgroups math pdf printable freekutasoftware.com has been visited by 10K+ users in the past month
teacherspayteachers.com has been visited by 100K+ users in the past month
Search results
Results from the WOW.Com Content Network
In mathematics, the lattice of subgroups of a group is the lattice whose elements are the subgroups of , with the partial ordering being set inclusion. In this lattice, the join of two subgroups is the subgroup generated by their union , and the meet of two subgroups is their intersection .
Let be a locally compact group and a discrete subgroup (this means that there exists a neighbourhood of the identity element of such that = {}).Then is called a lattice in if in addition there exists a Borel measure on the quotient space / which is finite (i.e. (/) < +) and -invariant (meaning that for any and any open subset / the equality () = is satisfied).
The intersection of subgroups A and B of G is again a subgroup of G. [5] For example, the intersection of the x-axis and y-axis in under addition is the trivial subgroup. More generally, the intersection of an arbitrary collection of subgroups of G is a subgroup of G.
The associated closure operator on subgroups of is ¯ =; the associated kernel operator on subgroups of / is the identity. A proof of the correspondence theorem can be found here . Similar results hold for rings , modules , vector spaces , and algebras .
In the second row are the maximal subgroups; their intersection (the Frattini subgroup) is the central element in the third row. So Dih 4 has only one non-generating element beyond e . In mathematics , particularly in group theory , the Frattini subgroup Φ ( G ) {\displaystyle \Phi (G)} of a group G is the intersection of all maximal subgroups ...
G is a supersolvable group with elementary abelian Sylow subgroups (a special type of A-group), (Hall 1937, Theorem 1 and 2). Later, in ( Zacher 1953 ), a group is said to be complemented if the lattice of subgroups is a complemented lattice , that is, if for every subgroup H there is a subgroup K such that H ∩ K = 1 and H , K is the whole group.
Hasse diagram of the Zassenhaus "butterfly" lemma – smaller subgroups are towards the top of the diagram. In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Zassenhaus, is a technical result on the lattice of subgroups of a group or the lattice of submodules of a module, or more generally for any modular lattice.
In mathematics, in the field of group theory, a modular subgroup is a subgroup that is a modular element in the lattice of subgroups, where the meet operation is defined by the intersection and the join operation is defined by the subgroup generated by the union of subgroups.
Ads
related to: lattice of subgroups math pdf printable freekutasoftware.com has been visited by 10K+ users in the past month
teacherspayteachers.com has been visited by 100K+ users in the past month