**
Salma
Shaheen,
Department
of
Pure
Mathematics,
University
of
Waterloo**

**
"Algebras
from
Finite
Group
Actions"**

In
1976,
S.
Eilenberg
and
M.-P.
Schützenberger
posed
the
following
Diabolical
question:
if
**
A**
is
a
finite
algebraic
structure,
Σ
is
the
set
of
all
identities
true
in
**
A**,
and
there
exists
a
finite
subset
F
of
Σ
such
that
F
and
Σ
have
exactly
the
same
*
finite*
models,
must
there
also
exist
a
finite
subset
F'
of
Σ
such
that
F'
and
Σ
have
exactly
the
same
*
finite
and
infinite*
models?
(That
is,
must
the
identities
of
**
A**
be
"finitely
based"?).
It
is
known
that
any
counter
example
to
their
question
must
be
inherently
nonfinitely
based
(INFB)
but
not
inherently
nonfinitely
based
in
the
finite
sense
(INFB*fin*).
In
this
talk,
I
will
show
that
the
algebras
constructed
by
Lawrence
and
Willard
from
group
action
do
not
provide
a
counter
example
to
this
question.
If
time
permits,
I
will
give
the
first
known
examples
of
inherently
nonfinitely
based
"automatic
algebras"
constructed
from
group
actions.

MC 5479