[UNKNOWN] Given a group G with infinite order, is it fast to find the inverse of any given element in G?
This question arose in one of my math classes today and no one knew the answer. Obviously, if G can also be written as a field, we can use the Extended Euclidean Algorithm. But what if the group can't be written as a field? Is there still a fast way to find the inverse?
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
good question, i have no answer though lol
@Zarkon @satellite73 @FoolForMath Have any ideas?
@UnkleRhaukus @imranmeah91 @myininaya @amistre64 @saifoo.khan @Mr.Math
Any ideas of if this true or not? And/or do you know who on here would be most likely to be able to help?
Not the answer you are looking for? Search for more explanations.
dr kiss would know im sure, this is sounds like her type of abstract algebra thing
I'm not sure I understand your question right, I don't know what exactly you mean by "fast way". This seems to be relative for how complex or simple is the group. For instance, it's very easy to find the inverse of a cyclic groups. Take for example the set of real numbers under addition or the set of positive rational numbers under multiplication. I hope I'm not off topic.
@across might be interested in this.
*to find the inverse of an element in a cyclic group*
I'm using "fast" as in polynomial time. For any finite group this is fast using successive squaring and Lagrange's Theorem, but if you're in an infinite group, we didn't know of any algorithm to find the inverse of an element.
In some infinite groups, like the rationals or the integers, it is easy to find the inverse since they're cyclic, or for a variety of other reason, but in others, is it still easy?