Equation 677 Database

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Magma 536b33eb002c…

magma 536b33eb002c
Size
321
Isomorphism class hash
536b33eb002cdc279be96422002b4d6791876a41ea68ac0e87746ece3de7c665
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 22:33:30
Display reorder
311,236,259,245,275,11,107,58,223,12,108,59,222,10,109,61,220,9,110,60,221,235,260,246,274,64,15,111,216,62,16,112,217,63,17,113,215,14,66,114,219,237,247,261,273,13,65,115,218,189,190,188,185,186,187,191,192,291,289,290,292,306,300,308,317,294,281,284,276,205,49,81,19,206,48,82,18,209,45,85,21,207,46,83,22,208,47,84,20,79,211,41,24,283,295,280,277,80,210,40,23,214,78,43,26,212,76,44,27,213,77,42,25,184,182,183,180,181,179,175,173,177,178,176,174,310,302,304,315,3,70,170,91,2,69,169,92,233,249,271,252,0,68,172,93,232,248,272,253,1,67,171,94,166,8,75,89,167,6,73,90,168,7,74,88,234,270,250,251,5,164,72,86,4,165,71,87,158,159,160,161,162,163,156,157,287,293,286,288,301,319,305,316,279,285,278,282,35,104,31,56,34,103,30,57,239,258,238,244,32,106,28,55,33,105,29,54,98,39,102,51,255,241,257,242,97,38,101,50,36,95,99,53,37,96,100,52,240,254,256,243,195,193,194,198,196,197,201,199,203,204,202,200,303,309,307,318,117,151,141,126,118,152,139,127,116,150,140,128,120,154,137,129,121,155,138,130,119,153,136,131,267,262,269,264,266,263,268,265,145,122,149,132,124,143,147,133,125,144,148,134,123,142,146,135,224,225,226,227,228,229,230,231,298,296,297,299,314,312,313,320 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#616ee92b4c2e3f87630606dae5e5d5a5d531c0e51b30b7b61db0c949f5d47644, 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 22:33:31 · history