Some necroposting here. I managed to get a look at that book (Player Companion: Weapon Master's Handbook) at my friend's place.
First thing's - some funny news.
There is no any form of table with fighter groups in that book. (be that complete or incomplete or both) I felt like my sanity started to seep away when I wrapped my head around that concept.
Even if you search it (that book) by automated methods to exclude human error, there only few mentions of "groups" word and in context where they used they have no relevance to our problem. Really.
Short summary of book:
Weapon design rules are quite complete - they take pages 28-29 and they are all listed at d20pfsrd.
Pages 30-31 has some rules for magic abilities for weapons but those have absolutely no correlation to "gnome flick-mace", "khakkhra", or "war flute".
Pages 1-27 can be loosely described as big list of feats and tricks. No there are no weapon groups there.
That was a puzzle interesting to solve. (Read: it was maddening) Thankfully, consumed by insanitypiration I started to Google different parts of sentences being not in a right frame of mind and that gave me important tip, which i think makes sense:
https://paizo.com/pathfinderRPG/prd/coreRulebook/classes/fighter.html
Weapon groups are defined as follows (GMs may add other weapons to
these groups, or add entirely new groups):
Axes: battleaxe, dwarven waraxe, greataxe, handaxe, heavy pick, light
pick, orc double axe, and throwing axe.
Blades, Heavy: bastard sword, elven curve blade, falchion, greatsword,
longsword, scimitar, scythe, and two-bladed sword.
Blades, Light: dagger, kama, kukri, rapier, sickle, starknife, and
short sword.
Bows: composite longbow, composite shortbow, longbow, and shortbow.
Close: gauntlet, heavy shield, light shield, punching dagger, sap,
spiked armor, spiked gauntlet, spiked shield, and unarmed strike.
Crossbows: hand crossbow, heavy crossbow, light crossbow, heavy
repeating crossbow, and light repeating crossbow.
> Double: dire flail, dwarven urgrosh, gnome hooked hammer, orc double
axe, quarterstaff, and two-bladed sword.
Flails: dire flail, flail, heavy flail, morningstar, nunchaku, spiked
chain, and whip.
Hammers: club, greatclub, heavy mace, light hammer, light mace, and
warhammer.
> Monk: kama, nunchaku, quarterstaff, sai, shuriken, siangham, and
unarmed strike.
Natural: unarmed strike and all natural weapons, such as bite, claw,
gore, tail, and wing.
Pole Arms: glaive, guisarme, halberd, and ranseur.
Spears: javelin, lance, longspear, shortspear, spear, and trident.
Thrown: blowgun, bolas, club, dagger, dart, halfling sling staff,
javelin, light hammer, net, shortspear, shuriken, sling, spear,
starknife, throwing axe, and trident.
Emphasis mine.
Here comes some small important detail - in the book of (Player Companion: Weapon Master's Handbook) they actually have Double and Monk as italic so that is written like:
Fighter Weapon Group: You must choose the fighter weapon group (or groups) to which your weapon belongs. When determining this, pick the
fighter weapon group with the most weapons that have similar
statistics (in the case of ranged weapons, the group with the most
weapons that are reloaded in the same manner). Some fighter weapon
groups grant weapons additional abilities, as noted below.
Double: The weapon gains the double special feature. You pick the damage type of each of the weapon's ends separately. If you choose the
additional damage type or the improved damage quality with the weapon
(see below), treat each end as a separate weapon when determining the
Design Point cost of that quality.
Monk: A weapon can be placed in the monk group only if it gains the monk weapon feature (see below).
Hands: For melee weapons, y...
Weight: When determining a weapon's...
So in the end I think in original it meant that you can choose any fighter's group from Fighter's Class page. But if that group is Double or Monk it will have additional abilities like:
Double: The weapon gains the double special feature. You pick the damage type of each of the weapon's ends separately. If you choose the
additional damage type or the improved damage quality with the weapon
(see below), treat each end as a separate weapon when determining the
Design Point cost of that quality.
Monk: A weapon can be placed in the monk group only if it gains the monk weapon feature (see below).
Any weapon of any other group (not from Double or Monk) is absolutely mundane and have no abilities you should worry about.
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https://stackoverflow.com/questions/1732348/regex-match-open-tags-except-xhtml-self-contained-tags#answer-1732454