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What about the definition: the set of algebraic group homomorphisms from $\mathbb C^*$ to $G$? 129.215.104.100 ( talk) 11:55, 19 September 2012 (UTC)
The phrase One-parameter group is often used to mean one-dimensional Lie group. At present, this article notes that a particular group homomorphism is being designated by the phrase, so that this particular kind of group is not a group. The structure of a "one-dimensional Lie group" is no different than that of the real line as a group under addition, so its features don't inspire an article. The analysis of the concept presently presented would be confusing to a general reader and verges on meta-mathematics. Given that the topic has a significant literature, there may be sources to fill the vacuum and counter the obfuscation of the non-group group. Rgdboer ( talk) 01:04, 10 January 2015 (UTC)
A link to usage by Sophus Lie in 1893 has been posted. Rgdboer ( talk) 03:11, 10 January 2015 (UTC)
"Discussion"
That means that it is not in fact a group,<ref "One-parameter group not a group? Why?", Stack Exchange Retrieved on 9 January 2015. /ref> strictly speaking;
That is, we start knowing only that
where , are the 'parameters' of group elements in . We may have
for some . This happens for example if is the unit circle and
In that case the kernel of consists of the integer multiples of .
Therefore a one-parameter group or one-parameter subgroup has to be distinguished from a group or subgroup itself, for the three reasons
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