Permutation IAPS

From Apstheory

Contents 1 Definition 1.1 Symbol-free definition 1.2 Definition with symbols 2 Property theory 2.1 Simplicity

Definition

Symbol-free definition

The permutation IAPS is an IAPS of groups where the Failed to parse (Can't write to or create math temp directory): n^{th}

member is the symmetric group Failed to parse (Can't write to or create math temp directory): S_n

, and where the block concatenation map Failed to parse (Can't write to or create math temp directory): S_m

× Failed to parse (Can't write to or create math temp directory): S_n
→ S_{m+n} is defined as the permutation that permutes the first Failed to parse (Can't write to or create math temp directory): m
symbols according to the left argument and the next Failed to parse (Can't write to or create math temp directory): n
symbols according to the second argument.

Definition with symbols

The permutation IAPS is an IAPS of groups where the Failed to parse (Can't write to or create math temp directory): n^{th}<math> member is <math>S_n

and the block concatenation map Failed to parse (Can't write to or create math temp directory): \\Phi_{m,n}: S_m
× Failed to parse (Can't write to or create math temp directory): S_n</mat> &rarr; <math>S_{m+n}
is defined as follows: (fillin)

Property theory

Simplicity