A word of length 4 in a local group, with two different values
I've been told that in a local group, one can find a word of length of $n=4$, i.e $w=g_1 g_2 g_3 g_4$, with two different meanings depending on how we put the parentheses. However I've also read that a well defined word has only one value, which means that I'm looking a word which is not well defined.
Can anyone give me a hint of such an example, or tell me whether my understanding of these basic facts is true?
group-theory topological-groups
asked Nov 27 at 11:15
Keen-ameteur
1,257316
add a comment |
I've been told that in a local group, one can find a word of length of $n=4$, i.e $w=g_1 g_2 g_3 g_4$, with two different meanings depending on how we put the parentheses. However I've also read that a well defined word has only one value, which means that I'm looking a word which is not well defined.
Can anyone give me a hint of such an example, or tell me whether my understanding of these basic facts is true?
group-theory topological-groups
asked Nov 27 at 11:15
Keen-ameteur
1,257316
Even a word of length 3 can have two different meanings in a local group if one of them is a value and the other is "not defined". Do you perhaps mean that a word of length 4 can have two different values rather than just two different meanings?
– C Monsour
Nov 27 at 18:38
I meant two different values, but I'm unsure as to why there is a difference? Assuming that every choice of parentheses is defined, doesn't local associativity imply a unique value?
– Keen-ameteur
Nov 27 at 18:45
In a local group, ab and (ab)c may be defined without bc being defined. That's why there's a difference.
– C Monsour
Nov 27 at 23:42
add a comment |
I've been told that in a local group, one can find a word of length of $n=4$, i.e $w=g_1 g_2 g_3 g_4$, with two different meanings depending on how we put the parentheses. However I've also read that a well defined word has only one value, which means that I'm looking a word which is not well defined.
Can anyone give me a hint of such an example, or tell me whether my understanding of these basic facts is true?
group-theory topological-groups
asked Nov 27 at 11:15
Keen-ameteur
1,257316
I've been told that in a local group, one can find a word of length of $n=4$, i.e $w=g_1 g_2 g_3 g_4$, with two different meanings depending on how we put the parentheses. However I've also read that a well defined word has only one value, which means that I'm looking a word which is not well defined.
Can anyone give me a hint of such an example, or tell me whether my understanding of these basic facts is true?
group-theory topological-groups
group-theory topological-groups
asked Nov 27 at 11:15
Keen-ameteur
1,257316
asked Nov 27 at 11:15
Keen-ameteur
1,257316
asked Nov 27 at 11:15
Keen-ameteur
1,257316
asked Nov 27 at 11:15
Keen-ameteur
1,257316
asked Nov 27 at 11:15
Keen-ameteur
1,257316
1,257316
Even a word of length 3 can have two different meanings in a local group if one of them is a value and the other is "not defined". Do you perhaps mean that a word of length 4 can have two different values rather than just two different meanings?
– C Monsour
Nov 27 at 18:38
I meant two different values, but I'm unsure as to why there is a difference? Assuming that every choice of parentheses is defined, doesn't local associativity imply a unique value?
– Keen-ameteur
Nov 27 at 18:45
In a local group, ab and (ab)c may be defined without bc being defined. That's why there's a difference.
– C Monsour
Nov 27 at 23:42
add a comment |
Even a word of length 3 can have two different meanings in a local group if one of them is a value and the other is "not defined". Do you perhaps mean that a word of length 4 can have two different values rather than just two different meanings?
– C Monsour
Nov 27 at 18:38
I meant two different values, but I'm unsure as to why there is a difference? Assuming that every choice of parentheses is defined, doesn't local associativity imply a unique value?
– Keen-ameteur
Nov 27 at 18:45
In a local group, ab and (ab)c may be defined without bc being defined. That's why there's a difference.
– C Monsour
Nov 27 at 23:42
Even a word of length 3 can have two different meanings in a local group if one of them is a value and the other is "not defined". Do you perhaps mean that a word of length 4 can have two different values rather than just two different meanings?
– C Monsour
Nov 27 at 18:38
Even a word of length 3 can have two different meanings in a local group if one of them is a value and the other is "not defined". Do you perhaps mean that a word of length 4 can have two different values rather than just two different meanings?
– C Monsour
Nov 27 at 18:38
I meant two different values, but I'm unsure as to why there is a difference? Assuming that every choice of parentheses is defined, doesn't local associativity imply a unique value?
– Keen-ameteur
Nov 27 at 18:45
I meant two different values, but I'm unsure as to why there is a difference? Assuming that every choice of parentheses is defined, doesn't local associativity imply a unique value?
– Keen-ameteur
Nov 27 at 18:45
In a local group, ab and (ab)c may be defined without bc being defined. That's why there's a difference.
– C Monsour
Nov 27 at 23:42
In a local group, ab and (ab)c may be defined without bc being defined. That's why there's a difference.
– C Monsour
Nov 27 at 23:42
add a comment |
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Even a word of length 3 can have two different meanings in a local group if one of them is a value and the other is "not defined". Do you perhaps mean that a word of length 4 can have two different values rather than just two different meanings?
– C Monsour
Nov 27 at 18:38
I meant two different values, but I'm unsure as to why there is a difference? Assuming that every choice of parentheses is defined, doesn't local associativity imply a unique value?
– Keen-ameteur
Nov 27 at 18:45
In a local group, ab and (ab)c may be defined without bc being defined. That's why there's a difference.
– C Monsour
Nov 27 at 23:42