Transactions of the AMS. Year 1969. Volume 146. Number 00.

$2$-transitive symmetric designs
William M. Kantor
1-28

Degree of symmetry of a product manifold
H. T. Ku; L. N. Mann; J. L. Sicks; J. C. Su
133-149

Principal cofibrations in the category of simplicial groups
Norbert H. Schlomiuk
151-165

Periodic solutions of hyperbolic partial differential equations in a strip
A. K. Aziz; A. M. Meyers
167-178

On an ordinary differential equation involving a convex function
Philip Hartman
179-202

Limit-operators and topological coreflections
Horst Herrlich
203-210

On hypersingular integrals and certain spaces of locally differentiable functions
Richard L. Wheeden
211-230

Partial prolongations and characteristics of differential equations.
H. H. Johnson
231-240

On the row convergence of the Walsh array for meromorphic functions.
E. B. Saff
241-257

Maximal abelian subalgebras of hyperfinite factors
Ole A. Nielsen
259-272

Classifying spaces and infinite symmetric products
M. C. McCord
273-298

The potential kernel and hitting probabilities for the general stable process in $R\sp{N}$
W. E. Pruitt; S. J. Taylor
299-321

Identities involving the coefficients of a class of Dirichlet series. III
Bruce C. Berndt
323-348

Two-parameter groups of formal power series
Abselom Ran
349-368

Abstract: By ${\Omega ^F}$ we denote the group of the formal power series having the form $ F(z) = \Sigma _{q = 1}^\infty {f_q}{z^q},{f_1} \ne 0$, with respect to formal composition of power series. The problem of analytic iteration leads to the study of subgroups of ${\Omega ^F}$, having the form $\displaystyle F(z,s) = \sum\limits_{q = 1}^\infty {{f_q}(s){z^q}}$ where the coefficients ${f_q}(s)$ are analytic functions of the complex parameter s, such that for any two complex numbers s and t the formal law of composition $\displaystyle F[F(z,s),t] = F(z,s + t)$ is valid [6], [8]. The purpose of the present paper is to study similar two-parameter subgroups of ${\Omega ^F}$. In §1 r-parameter analytic subgroups of $ {\Omega ^F}$ are defined, as well as other concepts connected with the problem. In §2 the importance of two-parameter subgroups is emphasized. It is shown that the number of parameters of analytic subgroups of $ {\Omega ^F}$ can always be reduced to two at most. The existence of a countable number of classes of the two-parameter subgroups of ${\Omega ^F}$ is shown. §3 gives the explicit form of the coefficients ${f_q}({a^1},{a^2})$ of a two-parameter subgroup of ${\Omega ^F}$: $\displaystyle F(z,{a^1},{a^2}) = \sum\limits_{q = 1}^\infty {{f_q}({a^1},{a^2}){z^q}} .$ In §4 the existence of canonical representations for two-parameter analytic subgroups of ${\Omega ^F}$ is proven, and it is shown that every two-parameter analytic subgroup of ${\Omega ^F}$ is globally isomorphic to one of the groups $\displaystyle {H_n}(z,{a^1},{a^2}) = (1 + {a^1})z/{(1 + {a^2}{z^n})^{1/n}},\quad n = 1,2, \ldots $ (no two of which are globally isomorphic to each other).

Transitive semigroup actions
C. F. Kelemen
369-375

Counterexamples in stable semigroups
L. O’Carroll
377-386

The first exotic class of a manifold
David L. Frank
387-395

Conjugate points and simple zeros for ordinary linear differential equations
Thomas L. Sherman
397-411

Extension and some applications of the coincidence theorems
Zalman Rubinstein; J. L. Walsh
413-427

Resolutions of singularities in prime characteristic for almost all primes
Paul C. Eklof
429-438

On the univalence of a certain integral
Mamoru Nunokawa
439-446

Embeddings of topological lattice-ordered groups
Robert L. Madell
447-455

A lemma in transcendental number theory
Robert Spira
457-464

Cohomology for ergodic groupoids
Joel J. Westman
465-471

On the number of multipications on ${\rm SU}(3)$ and ${\rm Sp}(2)$
Mamoru Mimura
473-492

The uniqueness of the Cauchy problem for partial differential equations which may have multiple characteristics
Peter M. Goorjian
493-509