Word Count : 524

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मान लीजिए (G) एक समूह है तथा (H) और (K), (G) के उपसमूह हैं। साथ ही (H') और (K'), क्रमशः (H) और (K) के प्रसामान्य उपसमूह हैं। हमें समूह समाकारिता के मूल प्रमेय की सहायता से ज़ासनहाउस (तितली) प्रमेयिका को सिद्ध करना है। सर्वप्रथम हम यह दिखाते हैं कि (H \cap K'), (H \cap K) का प्रसामान्य उपसमूह है। चूँकि (K'), (K) का प्रसामान्य उपसमूह है, अतः (K') का कोई भी संयुग्म (K') में ही रहता है। अब (H \cap K') के किसी भी तत्त्व (x) तथा ___ __________ __________ _______ __________ ___ ______.
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