G is a finite group with elements a and b. Let the conjugacy classes of these elements be A and B respectively and suppose |A|^2, |B|^2 < |G|. Prove that there is a non-identity element x in G s.t. x commutes with both a and b.
Conjugacy classes: symmetric and alternating groups. The conjugacy classes in Sn correspond to partitions of n, and are determined by cycle structure. ...
... See the attachment. This solution helps with questions involving conjugacy classes. ... n 12 It is known that an order k of any conjugacy class is a divisor of . ...
expressible as the union of conjugacy classes. ... (i) First, we prove that if H is a normal subgroup, then H is the union of conjugacy classes of G. ...
Conjugacy Classes. ... b) Let K1,....Kr be the conjugacy classes of G and for each Ki let Ki be the element of R[G] that is the sum of the members of Ki. ...
... Then the order of its conjugacy class is a divisor of =4. Therefore, it belongs to the class of the order 4. Hence coinsides with the subgroup {1} , where C is ...
