Equation 677 Database

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Magma 7b79a34f5f14…

magma 7b79a34f5f14
Size
707
Isomorphism class hash
7b79a34f5f14baea42a71b527bbbdc52d025d6c1a50d82529fd3d689816912cf
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 20:54:09
Display reorder
152,151,153,154,155,150,706,234,237,235,236,239,238,125,124,120,121,122,123,72,77,73,74,75,76,293,292,289,288,290,291,176,175,177,178,179,174,82,81,83,78,79,80,104,103,105,106,107,102,294,297,299,298,295,296,305,304,301,300,302,303,132,137,133,134,135,136,395,397,396,400,398,399,491,493,492,494,495,496,583,582,584,585,586,587,484,483,482,480,481,479,308,306,307,310,311,309,313,312,314,316,317,315,521,523,522,519,520,518,458,460,459,455,456,457,325,324,326,327,328,329,433,432,431,434,435,436,630,609,607,608,627,629,631,628,632,626,695,694,672,685,705,699,704,703,702,696,251,248,246,247,250,249,185,184,180,181,182,183,255,254,256,257,252,253,262,261,263,258,259,260,38,37,39,40,41,36,35,34,30,31,32,33,27,26,28,29,24,25,200,199,201,202,203,198,173,172,168,169,170,171,13,12,14,15,16,17,444,443,445,446,447,448,568,567,566,571,569,570,355,354,356,357,559,358,339,341,340,338,336,337,512,514,513,511,509,510,560,562,561,563,564,565,361,360,359,362,363,364,348,350,349,351,352,353,507,506,508,503,504,505,384,383,385,388,386,387,635,637,636,633,625,634,610,611,623,624,693,701,671,667,690,678,697,680,676,673,245,242,241,240,244,243,143,142,138,139,140,141,9,8,10,11,6,7,128,127,129,130,131,126,146,145,147,148,149,144,0,1,2,3,4,5,227,226,222,223,224,225,265,264,266,267,268,269,20,19,21,22,23,18,66,71,67,68,69,70,428,430,429,427,425,426,365,367,366,368,369,370,372,371,373,374,375,376,450,449,451,452,453,454,334,333,335,330,331,332,438,437,439,441,442,440,377,379,378,381,382,380,322,321,323,319,320,318,343,342,344,345,346,347,499,498,497,500,501,502,617,606,619,612,618,616,614,613,615,620,688,700,669,666,681,683,687,686,674,679,50,53,51,52,49,48,210,215,211,212,213,214,186,191,187,188,189,190,207,206,208,209,204,205,196,195,197,192,193,194,274,273,275,271,270,272,43,42,44,45,46,47,232,231,233,228,229,230,166,165,167,162,163,164,159,158,160,161,156,157,550,549,548,575,552,551,576,578,577,579,580,581,547,546,545,543,544,542,605,604,603,600,602,601,593,592,591,588,590,589,557,556,558,554,555,553,391,390,389,392,393,394,541,540,539,538,536,537,535,534,533,531,532,530,594,595,596,599,597,598,641,640,621,639,622,638,649,651,652,650,689,698,665,668,691,677,684,692,682,675,281,278,277,276,280,279,115,114,116,117,118,119,285,284,286,287,283,282,84,89,85,86,87,88,101,100,96,97,98,99,90,95,91,92,93,94,217,216,218,219,220,221,108,113,109,110,111,112,60,65,61,62,63,64,54,59,55,56,57,58,407,409,408,412,410,411,469,468,467,472,470,471,466,465,464,462,463,461,574,573,572,517,515,516,474,473,475,476,477,478,527,529,528,524,525,526,417,416,418,415,413,414,419,421,420,422,423,424,486,485,487,488,489,490,401,403,402,405,406,404,645,648,643,654,653,655,644,647,646,642,662,670,656,657,661,660,664,663,658,659 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 = {54, 55, 56, 57, 58, 59, 145} 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 20:54:10 · history