Men who become fathers later in life may pass a mark of longevity down to their paternal grandchildren.

He bad to open wyde his brazen gate, Which long time had bene shut, and out of hond Proclaymed joy and peace through all his state; For dead now was their foe which them forrayed late.

To the confusion and confounding of that cursed death's-head knight.

Theorem 10.5. The collection consisting of an invariant subgroup H and all its distinct cosets is itself a group, called the factor group of G, usually denoted by G/H. (Remember that the left and right cosets of an invariant subgroup are identical.) Multiplication of two cosets aH and bH is defined as the set of all distinct products z = xy, with x ∈ aH and y ∈ bH; the identity element of the factor group is the subgroup H itself.