Permutation IAPS
From Apstheory
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===Definition with symbols=== | ===Definition with symbols=== | ||
| - | The permutation IAPS is an [[IAPS of groups]] where the <math>n^{th}<math> member is <math>S_n</math> and the block concatenation map <math>\\Phi_{m,n}: S_m</math> × <math>S_n</ | + | The permutation IAPS is an [[IAPS of groups]] where the <math>n^{th}<math> member is <math>S_n</math> and the block concatenation map <math>\\Phi_{m,n}: S_m</math> × <math>S_n</math> → <math>S_{m+n}</math> is defined as follows: (fillin) |
==Property theory== | ==Property theory== | ||
===Simplicity=== | ===Simplicity=== | ||
Revision as of 01:00, 30 December 2006
Contents |
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
→ Failed to parse (Can't write to or create math temp directory): S_{m+n}
is defined as follows: (fillin)
