> The rule itself is referred to as "triple talaq" and is part of sharia. In Sunni islam, basically men can abandon women, without any (any) limit immediately and without consequences.
It's worth noting that there is no consensus on the validity or meaning of triple talaq within Sunni Islam.
> they get to take possession of everything the woman owns as well
This is not true, I guess you are confusing it with a khula divorce in which the woman requests that the man divorce her. In this case, she has to give back the mahr (bride price).
> They can take the kids if they want, including kids that have been conceived but not born yet (technically they should take the kids, but that's not what happens in practice).
In Islam kids stay with the woman if they are below a certain age, and men take kids above a certain age.
> Women face progressively harsher physical punishments for abandoning a man. If they remarry without his permission, they face (extra cruel) execution (stoning, often with the kids and family forced to watch).
I'm not sure what you mean, a woman does not need to seek permission to remarry from her ex-husband. Her current husband does need to give permission for a khula divorce, there are other kinds of divorce e.g. by a court in cases of mistreatment or abandonment. Yes, in general only men are given the right to divorce for no reason.
Stoning is the hadd punishment for adultery, i.e. sex with someone one is not married to.
It's worth noting that there is no consensus on the validity or meaning of triple talaq within Sunni Islam.
> they get to take possession of everything the woman owns as well
This is not true, I guess you are confusing it with a khula divorce in which the woman requests that the man divorce her. In this case, she has to give back the mahr (bride price).
> They can take the kids if they want, including kids that have been conceived but not born yet (technically they should take the kids, but that's not what happens in practice).
In Islam kids stay with the woman if they are below a certain age, and men take kids above a certain age.
> Women face progressively harsher physical punishments for abandoning a man. If they remarry without his permission, they face (extra cruel) execution (stoning, often with the kids and family forced to watch).
I'm not sure what you mean, a woman does not need to seek permission to remarry from her ex-husband. Her current husband does need to give permission for a khula divorce, there are other kinds of divorce e.g. by a court in cases of mistreatment or abandonment. Yes, in general only men are given the right to divorce for no reason.
Stoning is the hadd punishment for adultery, i.e. sex with someone one is not married to.