Equation 677 Database

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Magma 3c516bcf4438…

magma 3c516bcf4438
Size
205
Isomorphism class hash
3c516bcf44381dfce542b5a39a57ed21a9e4c35ba47f6cb3636211342fc65d83
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 204) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 06:03:16
Display reorder
200,201,202,203,204,151,58,149,156,109,59,93,47,111,60,94,48,113,53,96,33,115,54,98,34,35,55,117,100,32,56,119,102,146,57,106,104,31,24,26,11,13,15,19,9,67,108,95,81,68,110,97,82,61,112,99,77,62,114,101,78,63,116,103,79,80,118,64,105,147,148,65,150,157,107,66,92,30,25,27,10,12,14,18,8,128,76,143,37,130,69,145,38,132,70,154,83,152,71,159,52,121,72,135,50,51,73,123,137,49,74,124,139,36,75,126,141,29,22,23,7,4,5,17,6,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,163,161,160,162,167,165,164,166,171,169,168,170,199,195,196,198,192,193,194,197,43,127,85,140,44,129,86,142,45,131,87,144,46,133,88,155,39,153,89,158,134,120,40,90,136,122,41,91,138,125,42,84,28,21,20,2,3,0,16,1 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 205 = 5 + 5*40, 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#57ccc920f3a4ae4bbffe4b3ea9285a0b0b067889bdceee076361c43900c3431e, M = {40, 41, 42, 43, 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, 40): MacNeish's product over GF(8) x GF(5); GF(8) = F_2[x]/(x^3 + 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: 5.

last edited by qawbecrdtey at 2026-10-08 06:03:24 · history