Conjugate elements

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in a group

Elements and of for which

for some in . One also says that is the result of conjugating by . The power notation is frequently used for the conjugate of under .

Let be two subsets of a group , then denotes the set

For some fixed in and some subset of the set is said to be conjugate to the set in . In particular, two subgroups and are called conjugate subgroups if for some in . If a subgroup coincides with for every (that is, consists of all conjugates of all its elements), then is called a normal subgroup of (or an invariant subgroup, or, rarely, a self-conjugate subgroup).



[a1] B. Huppert, "Endliche Gruppen" , 1 , Springer (1967)
[a2] D. Gorenstein, "Finite groups" , Chelsea, reprint (1980)
How to Cite This Entry:
Conjugate elements. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article