You typically don't want to try appending to an array in .NET. It can be done, but it's expensive. In this case, you want to use a StringBuilder
Example:
StringBuilder sb = new StringBuilder();
if (abc.Checked)
{
//append lowercase abc
sb.Append(textbox1.Text.ToLower());
}
When you're done, you can get the string by calling sb.ToString(), or get the characters by calling sb.CopyTo().
Naming an array of strings "charArray" is very confusing.
Or are you trying to append strings, not append characters to a string? You want to use a List<string> for that, rather than a string[].
Example:
List<string> strings = new List<string>();
if (abc.Checked)
{
// append lowercase abc
strings.Add(textbox1.Text.ToLower());
}