  There is no consensus on the progenitors of Type Ia supernovae (SNe Ia)
despite their importance for cosmology and chemical evolution. We address this
question by using our previously published catalogs of Mg, Si, Ca, Cr, Fe, Co,
and Ni abundances in dwarf galaxy satellites of the Milky Way to constrain the
mass at which the white dwarf explodes during a typical SN Ia. We fit a simple
bi-linear model to the evolution of [X/Fe] with [Fe/H], where X represents each
of the elements mentioned above. We use the evolution of [Mg/Fe] coupled with
theoretical supernova yields to isolate what fraction of the elements
originated in SNe Ia. Then, we infer the [X/Fe] yield of SNe Ia for all of the
elements except Mg. We compare these observationally inferred yields to recent
theoretical predictions for two classes of Chandrasekhar-mass (M_Ch) SN Ia as
well as sub-M_Ch SNe Ia. Most of the inferred SN Ia yields are consistent with
all of the theoretical models, but [Ni/Fe] is consistent only with sub-M_Ch
models. We conclude that the dominant type of SN Ia in ancient dwarf galaxies
is the explosion of a sub-M_Ch white dwarf. The Milky Way and dwarf galaxies
with extended star formation histories have higher [Ni/Fe] abundances, which
could indicate that the dominant class of SN Ia is different for galaxies where
star formation lasted for at least several Gyr.
