Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 55736893d800…

magma 55736893d800
Size
705
Isomorphism class hash
55736893d8005757f00dc74cd21a27612f555270bf82d4dedbd3196e8a6ce031
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 15:58:13
Display reorder
660,89,312,356,448,370,87,313,354,449,371,88,314,355,447,369,315,85,359,444,366,316,86,357,445,367,317,84,358,446,368,95,310,362,454,376,93,311,360,455,377,94,309,361,453,375,306,91,365,450,372,307,92,363,451,373,308,90,364,452,374,686,679,673,677,17,256,198,262,484,15,257,199,263,485,16,255,200,261,483,252,13,201,258,480,253,14,202,259,481,254,12,203,260,482,8,247,196,268,490,6,248,197,269,491,7,246,195,267,489,250,11,192,264,486,251,9,193,265,487,249,10,194,266,488,669,662,665,671,278,472,382,550,210,276,473,383,551,211,277,471,381,549,212,468,281,378,546,213,469,279,379,547,214,470,280,380,548,215,273,478,388,556,208,274,479,389,557,209,275,477,387,555,207,474,272,384,552,204,475,270,385,553,205,476,271,386,554,206,678,675,680,683,168,228,0,410,405,169,229,2,408,406,170,230,1,409,407,231,171,4,413,404,232,172,5,411,402,233,173,3,412,403,174,646,647,648,645,175,654,655,656,653,176,638,639,640,637,612,177,613,617,616,622,178,623,624,620,630,179,631,632,628,703,697,704,699,46,418,496,329,96,47,419,497,327,97,45,417,495,328,98,414,42,492,325,99,415,43,493,326,100,416,44,494,324,101,37,424,502,320,102,38,425,503,318,103,36,423,501,319,104,420,40,498,323,105,421,41,499,321,106,422,39,500,322,107,690,693,692,689,157,460,216,290,538,158,461,217,288,539,156,459,218,289,537,456,160,219,293,534,457,161,220,291,535,458,159,221,292,536,163,466,222,285,544,164,467,223,286,545,162,465,224,287,543,462,166,225,284,540,463,167,226,282,541,464,165,227,283,542,663,667,668,661,56,129,430,141,341,54,130,431,142,339,55,131,429,143,340,128,59,426,140,337,126,57,427,138,338,127,58,428,139,336,51,120,436,132,332,52,121,437,133,330,53,122,435,134,331,123,50,432,135,335,124,48,433,136,333,125,49,434,137,334,695,691,696,694,72,586,604,348,148,73,587,605,349,149,74,585,603,350,147,582,75,600,351,144,583,76,601,352,145,584,77,602,353,146,78,592,610,346,154,79,593,611,347,155,80,591,609,345,153,588,81,606,342,150,589,82,607,343,151,590,83,608,344,152,685,688,682,674,60,440,18,598,532,61,438,19,599,533,62,439,20,597,531,443,63,21,594,528,441,64,22,595,529,442,65,23,596,530,66,649,644,651,650,67,657,652,659,658,68,641,636,643,642,619,69,618,615,614,625,70,621,627,626,633,71,629,635,634,700,698,701,702,191,574,508,31,241,189,575,509,32,242,190,573,507,30,240,570,187,504,34,244,571,188,505,35,245,572,186,506,33,243,182,580,514,29,239,180,581,515,27,237,181,579,513,28,238,576,185,510,25,235,577,183,511,26,236,578,184,512,24,234,670,666,672,664,118,305,394,520,562,119,303,395,521,563,117,304,393,519,561,301,114,390,516,558,302,115,391,517,559,300,116,392,518,560,109,296,400,526,568,110,294,401,527,569,108,295,399,525,567,299,112,396,522,564,297,113,397,523,565,298,111,398,524,566,687,676,684,681 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*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, 11, B) with E = magma#299bf89dcaadd64e33422b05a87b398de7449d556bda64ba0ca787ebaa3d1bcb, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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(11, 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: 45.

last edited by qawbecrdtey at 2026-10-03 15:58:15 · history