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 2 years ago
subgroup question
let G be an abelian group and H be a nonempty closed subset of G
prove that
 2 years ago
subgroup question let G be an abelian group and H be a nonempty closed subset of G prove that

This Question is Closed

walters
 2 years ago
Best ResponseYou've already chosen the best response.0\[H ^{*}=\left\{ xy ^{1}:x,y \in H \right\}\le G\]

myko
 one year ago
Best ResponseYou've already chosen the best response.0what the asterics H* means?

walters
 one year ago
Best ResponseYou've already chosen the best response.0it sort of another H (it can be any later ie Q)

myko
 one year ago
Best ResponseYou've already chosen the best response.0and by ≤ you mean that H* is a subset of G?

walters
 one year ago
Best ResponseYou've already chosen the best response.0i mean it is a subgroup

myko
 one year ago
Best ResponseYou've already chosen the best response.0it's vean long time since I did this, but I would try to prove the axioms for the elements of H* to be a abelian group: Closure: For all a, b in H*, the result of the operation a • b is also in H*. Associativity For all a, b and c in H*, the equation (a • b) • c = a • (b • c) holds. Identity element There exists an element e in H*, such that for all elements a in H*, the equation e • a = a • e = a holds. Inverse element For each a in H*, there exists an element b in H* such that a • b = b • a = e, where e is the identity element. CommutativityFor all a, b in H*, a • b = b • a.

myko
 one year ago
Best ResponseYou've already chosen the best response.0by the way, which operation respect to is this an abelian group?

walters
 one year ago
Best ResponseYou've already chosen the best response.0yes that one i get i want to show that 1 H* is not empty ie e element of H* 2 pq^1 element H* for every p,q element H*

walters
 one year ago
Best ResponseYou've already chosen the best response.01 H*\[\neq \] 2 let P,Q \[\in H ^{*}\]we want to show that PQ^1 element H*

walters
 one year ago
Best ResponseYou've already chosen the best response.0then PQ^1 =\[(xy ^{1})((xy ^{1}))^{1}\]

walters
 one year ago
Best ResponseYou've already chosen the best response.0=\[(xy ^{1})(x ^{1}y)=(xx ^{1})(yy ^{1})\]

walters
 one year ago
Best ResponseYou've already chosen the best response.0@terenzreignz pls help
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