True or False? 1. Let G be a group and H a nonempty subset of G. If ab-1 is in H whenever a and b are in H, then H is a subgroup of G. 2. 6Z

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True or False?<br>1.<br>Let G be a group and H a nonempty subset of G. If ab-1 is in H whenever a and b are in<br>H, then H is a subgroup of G.<br>2.<br>6Z < 3Z under addition.<br>3. Let G be a group and let a be one fixed element of G. Then the set {x € G| ax = xa} is a<br>subgroup of G.<br>

Extracted text: True or False? 1. Let G be a group and H a nonempty subset of G. If ab-1 is in H whenever a and b are in H, then H is a subgroup of G. 2. 6Z < 3z="" under="" addition.="" 3.="" let="" g="" be="" a="" group="" and="" let="" a="" be="" one="" fixed="" element="" of="" g.="" then="" the="" set="" {x="" €="" g|="" ax="xa}" is="" a="" subgroup="" of="">

Jun 05, 2022

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True or False? 1. Let G be a group and H a nonempty subset of G. If ab-1 is in H whenever a and b are in H, then H is a subgroup of G. 2. 6Z

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