Equation 677 Database

← all  ·  ← by size  ·  ← size 707

Magma 4880f790d33c…

magma 4880f790d33c
Size
707
Isomorphism class hash
4880f790d33c7adb02fd8cd792552d63578c30b8d17c729208e8f3dc8412ed96
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 20:44:02
Display reorder
532,531,530,528,529,527,640,207,206,208,209,204,205,203,200,198,199,202,201,102,107,103,104,105,106,109,108,110,111,112,113,185,184,180,181,182,183,274,273,275,271,270,272,263,262,259,258,260,261,268,267,269,265,264,266,38,37,39,40,41,36,122,121,123,124,125,120,313,317,312,314,315,316,490,489,491,488,486,487,504,506,505,509,507,508,335,334,333,330,332,331,485,484,483,480,481,482,437,436,435,432,433,434,413,412,411,409,410,408,439,438,440,443,441,442,545,547,546,550,548,549,554,556,555,551,552,553,619,622,623,620,624,621,637,645,647,701,670,678,699,677,696,700,691,702,706,705,236,235,237,238,239,234,96,99,97,98,101,100,31,30,32,33,34,35,21,20,22,23,18,19,128,127,129,130,131,126,27,26,28,29,24,25,0,1,2,3,4,5,284,283,285,286,287,282,215,214,210,211,212,213,151,150,152,153,154,155,114,119,115,116,117,118,346,345,347,344,342,343,590,588,589,592,593,591,472,471,473,468,469,470,401,400,399,396,397,398,389,388,387,384,385,386,403,402,404,405,406,407,390,392,391,394,395,393,382,381,383,378,379,380,449,448,447,446,444,445,629,618,638,639,649,648,641,635,642,681,675,690,683,664,674,673,666,682,688,698,86,85,87,88,89,84,61,64,62,63,60,65,142,141,143,138,139,140,146,145,147,148,149,144,244,243,245,240,241,242,70,69,71,66,67,68,288,289,290,291,292,293,49,48,50,51,52,53,57,56,58,59,54,55,133,132,134,135,136,137,93,92,94,95,90,91,356,355,354,357,358,359,417,419,418,416,414,415,375,377,376,374,372,373,349,348,350,353,351,352,423,425,424,421,422,420,575,574,573,571,572,570,603,605,604,600,602,601,561,563,562,560,558,559,537,536,538,534,535,533,607,646,628,644,625,630,636,643,633,686,680,692,687,657,671,684,662,689,676,697,45,44,46,47,42,43,219,216,220,221,218,217,9,8,10,11,6,7,301,305,300,302,303,304,79,78,80,81,82,83,307,306,308,309,310,311,276,281,277,278,279,280,76,75,77,72,73,74,233,232,228,229,230,231,222,227,223,224,225,226,295,299,294,296,297,298,578,576,577,579,580,581,467,466,465,463,464,462,458,457,456,460,461,459,569,568,567,565,564,566,587,586,585,583,582,584,360,362,361,365,363,364,369,371,370,367,368,366,454,453,455,450,451,452,599,598,597,596,595,594,631,627,614,632,626,606,634,651,650,704,665,679,703,661,672,685,663,693,694,695,163,162,164,165,166,167,257,252,253,256,255,254,192,197,193,194,195,196,17,16,12,13,14,15,326,328,327,324,325,329,160,159,161,156,157,158,170,169,171,172,173,168,321,320,322,323,319,318,251,250,247,246,248,249,175,174,176,177,178,179,189,188,190,191,186,187,474,476,475,478,479,477,522,521,523,524,525,526,540,539,541,542,543,544,338,337,336,339,340,341,428,427,426,429,430,431,557,513,514,510,511,512,502,501,503,500,498,499,495,497,496,494,492,493,516,515,517,519,520,518,615,609,617,616,610,612,613,611,608,668,656,658,669,653,654,655,652,659,660,667 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#96b028d3c6de0cbaff964417289f690895c6af42769867ad5a7d2affbed8a752, M = {72, 73, 74, 75, 76, 77, 126} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); 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: 101.

last edited by qawbecrdtey at 2026-10-07 20:44:03 · history