Voltage regulator location

I have an Ariens riding mower model 936042-00 powered by a B&S 20HP twin engine model 406777-0442-B1. Here is my dilemma. The engine is no longer charging the battery. I can measure the alternator and it puts out 27.4 VAC and 10.3 VDC. I would also like to check the regulator but cannot find it anywhere and I looked, believe me I looked. it is not on the shroud near the starter or anywhere else for that matter. Somebody told me that it probably doesn't have one, but is built in to the alternator or mounted together next to the alternator. Not so. I popped the flywheel and all I can see is the alternator ring. With all shrouds removed I still don't see anything resembling a voltage regulator. Can anybody shed some light on this. Even B&S has not been of any help. I don't even know what regulator to order. There are 2 listed for this engine. All very confusing. Help!

Thank you Roy. Now things starting to make sense. You are absolutely correct. There is a diode (lump) in the red line close to the white connector coming from the alternator which I will check tomorrow to see if its blown. What is the correct way to test the alternator for proper output voltage? I believe the correct alternator for my engine is part number 592831 in case I need to replace it. Do you agree?

Thanks AVB. I am learning fast and trying to put 2 and 2 together. Y'all correct me if I am wrong. I understand that on a system with a separate regulator the way to check the alternator output is to disconnect the alternator (white plug) run the engine at full throttle and the voltage at the plug should be 30 VAC or more. That voltage will then go to the regulator where it is converted and regulated to about 13.8 VDC or something like that. But since I don't have a voltage regulator in the conventional sense, the alternator still initially produces AC voltage but puts out the proper DC voltage at the white connector because of the inline diode. Am I correct so far? I did some more thorough checking today and here is what I found. I checked the inline diode and found it to be in order (dead in one direction and throughput in the other). While I was at it I checked the alternator output before the diode and it was a convincing 46.5 VAC (and nothing at the VDC setting, which of course there shouldn't be). Now I checked the voltage after the diode at the white (still disconnected) plug and it showed 11.3 V on the AC setting of my voltmeter and 23.6 V on the DC setting. Now I tested the charging voltage at the battery posts after everything was back reconnected and normal and the reading was 5.6 VDC. Battery posts and cables are clean and make good contact. The battery voltage by itself was 12.3 VDC. Tomorrow I will attempt to trace and check all the wiring, its connectors, fuses, ground connections etc. for corrosion and other short comings. In the meantime all good ideas are appreciated.
Thanks Rick

Matter of fact with engine not running and the ignition in run position there should be the battery voltage at the connector.
 
AVB, I performed the voltage check as you suggested above, but the voltage was Zero, strangely enough. But I also did a complete cleaning up of all the wiring, all connectors, all fuse holders with compressed air, removed ground wires and brushed surfaces with a wire brush to make sure we have good ground and low and behold that seemed to have fixed it. I now have 13.5 VDC charging power, done 3 days of mowing and the battery is still chuck full (12.9 VDC). I must add though that I had to replace the battery. It was really FUBAR. It would not accept one volt of charging and when I connected the charger to it it did some nasty sparking, almost like if I had the polarity mixed up or there was a short. Anyway, the problem seems to be fixed and everything is back to normal. I guess nothing that some serious maintenance and cleaning couldn't fix. Thanks y'all for your valuable help.