Assuming you have not completely lost touch with one another (for example, if you moved to another state without her knowledge), then it would be difficult, though not impossible, for her to get divorced without you knowing. To check, you would need to contact the clerk of court in whatever county she resided. Simply check on any filings in your name or in her name. Or, if you prefer, you could do a simple on-line search for the clerks website, most such sites include a search function to locate cases.
As to whether she has done anything illegal, if she has married another man while still married to you, then yes, she has done something illegal. Bigamy is defined as getting married to a person while already married to another. So yes, if you are still married and she has married another, then she could be charged with bigamy.
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