Equation 677 Database

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Magma 8a89e7c57481…

magma 8a89e7c57481
Size
321
Isomorphism class hash
8a89e7c574817ab16366bd4761fde1c04250161462dab33c19de8ca568be5839
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:26:47
Display reorder
300,37,154,218,226,76,38,77,155,216,227,36,75,153,217,225,150,40,72,221,222,151,41,73,219,223,39,152,74,220,224,43,160,82,244,246,44,161,83,248,250,42,159,81,241,242,156,46,78,229,230,232,157,47,79,234,158,45,80,236,238,315,314,303,304,6,268,271,270,269,7,273,272,275,274,8,264,265,266,267,252,9,253,255,254,256,10,257,259,258,11,260,261,262,263,4,293,292,295,294,5,297,296,298,299,3,289,288,290,291,277,1,276,279,278,283,281,0,280,282,285,2,284,287,286,319,317,320,318,90,182,190,202,35,91,33,180,191,203,92,34,181,189,201,185,93,31,186,198,183,94,32,187,199,95,184,30,188,200,88,177,26,196,208,89,178,24,197,209,87,179,25,195,207,176,84,29,192,204,193,174,85,27,205,175,86,28,194,206,311,308,307,306,23,165,50,214,96,21,97,166,48,215,22,98,167,49,213,164,19,99,53,210,162,20,100,51,211,18,163,101,52,212,14,171,247,56,245,12,172,251,54,249,13,173,243,55,240,170,17,231,59,228,57,168,15,235,233,169,16,239,58,237,313,301,316,309,60,140,111,125,131,61,129,138,112,123,62,130,139,113,124,143,63,127,110,121,141,64,128,108,122,65,142,126,109,120,66,146,137,102,116,67,144,135,103,114,68,145,136,104,115,149,69,133,105,119,106,147,70,134,117,148,71,132,107,118,305,302,310,312 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#2ec821928dae411f986b7c636eee0f3d0451d16a0e775a52641e8351195889f9, M = {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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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 22:26:47 · history