Equation 677 Database

← all  ·  ← by size  ·  ← size 707

Magma a8d5bae538ff…

magma a8d5bae538ff
Size
707
Isomorphism class hash
a8d5bae538ff0d1f7d81efb8f9e2713c1b4970df61198e0c3ddeffe4b3d8d7b4
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
2026-10-08 10:20:17
Display reorder
577,579,578,576,574,575,647,14,17,15,16,13,12,34,33,35,30,31,32,174,173,175,176,177,172,198,197,199,200,201,196,184,189,185,186,187,188,215,214,216,217,212,213,287,306,246,265,301,266,305,273,291,283,276,277,297,261,218,219,220,221,60,65,61,62,63,64,19,18,20,21,22,23,599,598,597,596,595,594,390,389,388,392,393,391,556,555,557,558,559,560,395,394,396,397,398,399,336,335,337,339,340,338,346,345,344,341,342,343,437,436,438,440,441,439,443,442,444,445,446,447,423,422,421,418,419,420,636,637,607,608,638,614,630,639,635,685,691,656,667,698,706,705,703,695,704,696,308,280,293,285,274,281,303,269,248,249,250,251,253,252,254,270,309,289,295,259,146,147,144,145,138,143,139,140,141,142,68,67,69,70,71,66,2,0,3,4,5,1,160,165,161,162,163,164,83,82,78,79,80,81,152,151,153,148,149,150,77,76,72,73,74,75,352,351,350,349,347,348,562,561,563,564,565,566,521,520,522,523,524,525,369,368,370,365,366,367,405,404,403,402,400,401,510,509,508,511,512,513,387,386,385,384,382,383,375,374,376,371,372,373,536,535,534,587,532,533,613,629,609,612,606,610,632,634,611,668,697,659,657,673,688,687,692,669,689,678,55,58,56,57,54,59,29,28,24,25,26,27,9,8,10,11,6,7,192,191,193,194,195,190,179,178,180,181,182,183,210,209,211,206,207,208,267,288,302,247,268,307,278,284,279,272,304,292,296,260,202,203,204,205,53,52,48,49,50,51,169,168,170,171,166,167,406,408,407,409,410,411,334,333,332,331,330,573,585,584,586,582,581,583,414,413,412,416,417,415,353,355,354,356,357,358,429,428,427,424,425,426,449,448,450,453,452,451,603,605,604,602,601,600,433,435,434,431,432,430,627,628,641,625,619,626,618,617,640,680,701,660,661,682,694,699,675,676,681,674,226,229,227,228,231,230,271,257,310,290,255,256,298,262,222,223,224,225,245,244,263,299,264,300,294,311,286,282,258,275,158,157,159,154,155,156,234,233,235,236,237,232,37,36,38,39,40,41,43,42,44,45,46,47,108,113,109,110,111,112,103,102,104,105,106,107,545,544,543,548,546,547,589,588,590,591,592,593,553,552,554,549,550,551,380,379,381,377,378,580,568,567,569,571,572,570,541,540,542,539,537,538,529,531,530,526,527,528,517,519,518,516,514,515,361,360,359,362,363,364,623,621,616,615,622,624,631,633,620,702,690,655,679,683,693,700,677,684,686,670,85,88,86,87,84,89,91,90,92,93,94,95,313,317,312,314,315,316,321,320,322,323,319,318,121,120,122,123,124,125,129,128,130,131,126,127,117,116,118,119,114,115,136,135,137,132,133,134,97,96,98,99,100,101,328,327,329,325,324,326,238,243,239,240,241,242,460,462,461,463,464,465,500,499,501,496,497,498,488,487,489,484,485,486,480,479,478,482,483,481,468,467,466,471,469,470,476,475,477,474,472,473,459,458,457,456,454,455,504,503,502,506,507,505,490,492,491,494,495,493,642,651,643,648,645,644,650,646,649,663,672,652,653,664,665,671,662,658,666,654 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#92768bb2ce71adf5f3645437d2daad1854a25afcd5bf6e7bdc519de5c37f97ae, M = {66, 67, 68, 69, 70, 71, 130} 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 2026-10-08 10:20:18 · history