Nilpotent Groups
نویسندگان
چکیده
The articles [2], [3], [4], [6], [7], [5], [8], [9], [10], and [1] provide the notation and terminology for this paper. For simplicity, we use the following convention: x is a set, G is a group, A, B, H, H1, H2 are subgroups of G, a, b, c are elements of G, F is a finite sequence of elements of the carrier of G, and i, j are elements of N. One can prove the following propositions: (1) ab = a · [a, b]. (2) [a, b]−1 = [a, b−1]. (3) [a, b]−1 = [a−1, b]. (4) ([a, b−1])−1 = [b−1, a]. (5) [a, b−1, c] = [[a, b−1], cb]. (6) [a, b−1] = [b, a]. (7) [a, b−1, c] = [b, a, cb]. (8) [a, b, ca] · [c, a, bc] · [b, c, ab] = 1G. (9) [A,B] is a subgroup of [B,A].
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ورودعنوان ژورنال:
- Formalized Mathematics
دوره 18 شماره
صفحات -
تاریخ انتشار 2010