For optical isomerism chiral carbon should be present i.e. carbon with four different groups but this compound doesn't have one then why does it show optical isomerism?

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    $\begingroup$ For optical isomerism, a molecule should be different from its mirror image; that's all. Whether it contains a chiral carbon (or any carbon at all, for that matter) is irrelevant. $\endgroup$ – Ivan Neretin Oct 8 '20 at 16:54
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    $\begingroup$ @Maurice Glycine is the achiral amino acid since there is no carbon center with 4 different substituents (R = H). $\endgroup$ – Zhe Oct 8 '20 at 16:57
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    $\begingroup$ @AY The key here is to ask how the glycines are arranged around the central nickel atom. If the arrangement breaks enough symmetry, then the complex is not superimposable on its mirror image. $\endgroup$ – Zhe Oct 8 '20 at 16:59
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    $\begingroup$ Dear anonymous editor, please stop submitting edits that attempt to change gly into a sum formula. For one, gly is easier to read and understand. For two, the sum formula you are suggesting is outright wrong. For three, MathJax should not be used in titles anyway (but that only applies to the question). $\endgroup$ – Jan Oct 16 '20 at 13:29
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    $\begingroup$ On this site we aim to have high quality questions and answers. Every user has the ability to edit posts, or suggest such edits. In the latter case they will be reviewed by more experienced users. Editing can have multiple reasons, some are introducing better formatting, correcting spelling, adding tags, giving a better title, etc.. Please take the tour to find out more about this site and if you have more questions related to that, visit Chemistry Meta. Unfortunately, you question has been targeted by an anonymous editor for a while. I hope that is over now. $\endgroup$ – Martin - マーチン Oct 20 '20 at 18:18

Your assumption that $\ce{[Ni(gly)2]}$ shows optical isomerism is incorrect: the complex is square planar in nature and has a plane of symmetry (the plane passing through all the atoms). It is thus achiral and does not have any optical isomers.

It does show geometrical isomerism though, as the ligands are not symmetric with reference to each other.

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