Equation 677 Database

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Magma 8bee4bd1608c…

magma 8bee4bd1608c
Size
273
Isomorphism class hash
8bee4bd1608ca3559796c97e887a2405a1f3d74fd96c74bab5b94ba7bf9f2738
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 272) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 22:41:55
Display reorder
145,146,144,148,149,147,151,152,150,154,155,153,253,139,160,38,228,140,36,229,161,138,159,37,230,142,156,41,231,143,157,39,232,141,158,40,233,137,166,44,234,135,167,42,235,136,165,43,236,133,162,47,237,134,163,45,238,132,164,46,239,266,260,259,265,221,175,67,130,219,68,131,176,220,174,66,129,217,178,70,126,218,179,71,127,216,177,69,128,227,173,65,121,225,171,63,122,226,172,64,120,223,169,61,124,224,170,62,125,222,168,60,123,258,264,263,257,76,13,28,182,77,29,180,14,75,12,27,181,72,16,24,185,73,17,25,183,74,15,26,184,82,19,34,188,83,20,35,186,81,18,33,187,78,22,30,191,79,23,31,189,80,21,32,190,261,271,272,262,49,118,206,243,50,204,244,119,48,117,205,245,52,114,209,242,53,115,207,240,51,116,208,241,55,109,212,247,56,110,210,248,54,108,211,249,58,112,215,250,59,113,213,246,57,111,214,251,267,270,269,268,199,91,4,96,200,5,97,92,198,90,3,98,202,94,1,99,203,95,0,100,201,93,2,101,197,89,10,102,195,87,11,103,196,88,9,104,193,85,6,105,194,86,7,106,192,84,8,107,256,252,255,254 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 273 = 13 + 5*52, 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#58222ccd0574e7adf03b9b32a848bfc3e464df8d7127a3e76f96a819fe65341a, M = {0, 5, 10, 16, 21, 26, 30, 35, 40, 45, 50, 55, 60} 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, 52): MacNeish's product over GF(4) x GF(13); 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 2026-10-06 22:41:56 · history