Malnormal subgroup explained

H

of a group

G

is termed malnormal if for any

x

in

G

but not in

H

,

H

and

xHx-1

intersect in the identity element.[1]

Some facts about malnormality:

When G is finite, a malnormal subgroup H distinct from 1 and G is called a "Frobenius complement".[4] The set N of elements of G which are, either equal to 1, or non-conjugate to anyelement of H, is a normal subgroup of G, called the "Frobenius kernel", and G is the semi-direct product of H and N (Frobenius' theorem).[5]

Notes and References

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