1
绗竴绔犱唬鏁板熀鏈蹇?/p>
1.
濡傛灉缇?/p>
G
涓?/p>
,
瀵逛换鎰忓厓绱?/p>
a,b
鏈?/p>
(ab)
2
=a
2
b
2
,
鍒?/p>
G
涓轰氦鎹㈢兢
.
璇佹槑
:
瀵逛换鎰?/p>
a,bG,
鐢辩粨鍚堝緥鎴戜滑鍙緱鍒?/p>
(ab)
2
=a(ba)b, a
2
b
2
=a(ab)b
鍐嶇敱宸茬煡鏉′欢浠ュ強娑堝幓寰嬪緱鍒?/p>
ba=ab,
鐢辨鍙缇?/p>
G
涓轰氦鎹㈢兢
.
2.
濡傛灉缇?/p>
G
涓?/p>
,
姣忎釜鍏冪礌
a
閮介�傚悎
a
2
=e,
鍒?/p>
G
涓轰氦鎹㈢兢
.
璇佹槑
: [
鏂规硶
1]
瀵逛换鎰?/p>
a,bG,
ba=bae=ba(ab)
2
=ba(ab)(ab)
=ba
2
b(ab)=beb(ab)=b
2
(ab)=e(ab)=ab
鍥犳
G
涓轰氦鎹㈢兢
.
[
鏂规硶
2]
瀵逛换鎰?/p>
a,bG,
a
2
b
2
=e=(ab)
2
,
鐢变笂涓�棰樼殑缁撹鍙煡
G
涓轰氦鎹㈢兢
.
3.
璁?/p>
G
鏄竴闈炵┖鐨勬湁闄愰泦鍚?/p>
,
鍏朵腑瀹氫箟浜嗕竴涓箻娉?/p>
ab,
閫傚悎鏉′欢
:
(1)
a(bc)=(ab)c;
(2)
鐢?/p>
ab=ac
鎺ㄥ嚭
a=c;
(3)
鐢?/p>
ac=bc
鎺ㄥ嚭
a=b;
璇佹槑
G
鍦ㄨ涔樻硶涓嬫垚涓�缇?/p>
.
璇佹槑
:[
鏂规硶
1]
璁?/p>
G={a
1
,a
2
,鈥?a
n
},k
鏄?/p>
1,2,鈥?n
涓煇涓�涓暟瀛?/p>
,
鐢?/p>
(2)
鍙煡鑻?/p>
ij(I,j=1,2,鈥?n),鏈?/p>
a
k
a
i
a
k
a
j
------------<1>
a
i
a
k
a
j
a
k
------------<2>
鍐嶇敱涔樻硶鐨勫皝闂�у彲鐭?/p>
G={a
1
,a
2
,鈥?a
n
}={a
k
a
1
, a
k
a
2
,鈥? a
k
a
n
}------------<3>
G={a
1
,a
2
,鈥?a
n
}={a
1
a
k
, a
2
a
k
,鈥? a
n
a
k
}------------<4>
鐢?/p>
<1>
鍜?/p>
<3>
鐭ュ浠绘剰
a
t
G,
瀛樺湪
a
m
G,
浣垮緱
a
k
a
m
=a
t
.
鐢?/p>
<2>
鍜?/p>
<4>
鐭ュ浠绘剰
a
t
G,
瀛樺湪
a
s
G,
浣垮緱
a
s
a
k
=a
t
.
鐢变笅涓�棰樼殑缁撹鍙煡
G
鍦ㄨ涔樻硶涓嬫垚涓�缇?/p>
.
涓嬮潰鐢ㄥ彟涓�绉嶆柟娉曡瘉鏄?/p>
,
杩欑鏂规硶鐪嬭捣鏉ユ湁浜涢暱浣嗘�濊矾姣旇緝娓呮銆?/p>
[
鏂规硶
2]
涓轰簡璇佹槑
G
鍦ㄧ粰瀹氱殑涔樻硶杩愮畻涓嬫垚涓�缇わ紝鍙璇佹槑
G
鍐呭瓨鍦ㄥ购鍏?/p>
(
鍗曚綅鍏?/p>
)
锛屽苟涓旇瘉鏄?/p>
G
鍐呮瘡涓�涓厓绱犻兘鍙�嗗嵆鍙?/p>
.
涓轰簡鍙欒堪鏂逛究鍙
G={a
1
,a
2
,鈥?a
n
}.