# Accession Number:

## AD0731479

# Title:

## Maximal Groups of Permutations and Complementations of the Independent Variables Which Leave a Set of Boolean Functions Invariant,

# Descriptive Note:

# Corporate Author:

## ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB

# Personal Author(s):

# Report Date:

## 1971-09-01

# Pagination or Media Count:

## 129.0

# Abstract:

The group of permutations and complementations, G sub n, is important in switching and automata theory. Elements of this group act on Boolean functions by complementing andor permuting their variables. A subgroup of G sub n is said to fix a set of n variable Boolean functions if every member of the subgroup leaves every function in the set invariant. The author defines the group of symmetries for the set of n variable Boolean functions fixed by a cyclic subgroup of G sub n to be the largest subgroup of G sub n which fixes every function in the set. Theorems are proved which enable one to determine completely the group of symmetries for the set of functions fixed by any cyclic subgroup of G sub n. In some instances the group of symmetries is larger than the cyclic subgroup and in others it is equal to the cyclic subgroup. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics