4. (a) Show that every group of order 4 is isomorphic to either Z4 or V4. (b) Show that H {1, (12)(34), (13)(24), (14)(23)} is a subgroup of S4, then use part (a show H is isomorphic to V.

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need some help with attached showing groups order 4 are isomorphic Z_4 or V_4 attached

4. (a) Show that every group of order 4 is isomorphic to either Z4 or V4.
(b) Show that H = {1,(12)(34), (13)(24), (14)(23)} is a subgroup of S4, then use part (a) to
show H is isomorphic to V4.
Transcribed Image Text:4. (a) Show that every group of order 4 is isomorphic to either Z4 or V4. (b) Show that H = {1,(12)(34), (13)(24), (14)(23)} is a subgroup of S4, then use part (a) to show H is isomorphic to V4.
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