Equation 677 Database

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Magma 79e8c0fd8c75…

magma 79e8c0fd8c75
Size
221
Isomorphism class hash
79e8c0fd8c75b8914b02a60448f54bc6d4a512ac306ae5bd1556d8026287795f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 220) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:14:35
Display reorder
220,172,171,173,174,175,168,169,170,110,130,150,11,31,51,71,95,56,76,91,116,137,156,16,35,120,140,1,21,40,60,80,100,5,25,45,65,85,105,125,146,206,211,215,201,186,185,187,188,189,190,191,184,113,133,153,14,34,54,74,98,58,78,93,119,139,159,19,39,124,144,4,24,43,64,84,104,8,29,49,69,89,109,129,149,208,214,219,204,160,161,162,163,164,165,166,167,111,131,151,10,30,50,70,96,55,75,90,115,136,157,15,36,122,142,2,22,42,62,82,102,7,27,47,67,87,107,127,147,207,210,217,202,196,195,197,198,199,192,193,194,114,134,154,13,33,53,73,99,59,79,94,118,138,158,18,38,123,143,3,23,44,63,83,103,9,28,48,68,88,108,128,148,209,213,218,203,183,182,176,177,178,179,180,181,112,132,152,12,32,52,72,97,57,77,92,117,135,155,17,37,121,141,0,20,41,61,81,101,6,26,46,66,86,106,126,145,205,212,216,200 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 221 = 1 + 5*44, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#a97cd359209ca8128895583745774fa637e4d6ff9668d716e70c1186faf8de63, M = {44} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 44): MacNeish's product over GF(4) x GF(11); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-01 22:14:36 · history