They belongs to the same class means
b is conjugate to a iff at least one x exist in G such that
b=xax–¹
–
Rohit Singh
·
1 year, 9 months ago

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Two elements \(x,y \in G\) are left congruent modulo the subgroup \(H\) if \(x^{-1}y \in H\), namely if \(xH = yH\), so that \(x\) and \(y\) define the same left coset. Left congruence is an equivalence relation on \(G\) - the decomposition of \(G\) into a disjoint union of equivalence classes (left cosets) gives us Lagrange's Theorem (when \(G\) is finite).

Two elements \(x,y \in G\) are right congruent modulo \(H\) if \(xy^{-1} \in H\), namely if \(Hx = Hy\), so that \(x\) and \(y\) define the same right coset. Right congruence is another equivalence relation on \(G\), which is different to left congruence unless the subgroup is normal.
–
Mark Hennings
·
3 years, 11 months ago

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TopNewestThey belongs to the same class means b is conjugate to a iff at least one x exist in G such that b=xax–¹ – Rohit Singh · 1 year, 9 months ago

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Two elements \(x,y \in G\) are

leftcongruent modulo the subgroup \(H\) if \(x^{-1}y \in H\), namely if \(xH = yH\), so that \(x\) and \(y\) define the same left coset. Left congruence is an equivalence relation on \(G\) - the decomposition of \(G\) into a disjoint union of equivalence classes (left cosets) gives us Lagrange's Theorem (when \(G\) is finite).Two elements \(x,y \in G\) are

rightcongruent modulo \(H\) if \(xy^{-1} \in H\), namely if \(Hx = Hy\), so that \(x\) and \(y\) define the same right coset. Right congruence is another equivalence relation on \(G\), which is different to left congruence unless the subgroup is normal. – Mark Hennings · 3 years, 11 months agoLog in to reply