Equation 677 Database

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Magma 23dbe2bf3a6f…

magma 23dbe2bf3a6f
Size
707
Isomorphism class hash
23dbe2bf3a6ffd1c3189306f620e02e256fe227eaaa0edd4637da63bd1f889f9
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
2026-10-06 21:53:59
Display reorder
546,545,547,550,548,549,633,202,201,203,198,199,200,108,109,110,111,112,113,298,297,299,294,295,296,248,247,249,250,251,246,291,290,292,293,288,289,97,96,98,99,100,101,104,103,105,106,107,102,81,80,82,83,78,79,157,159,161,160,156,158,196,195,197,192,193,194,310,309,311,306,307,308,422,421,420,425,423,424,356,355,354,358,359,357,495,494,496,492,493,491,349,348,350,353,351,352,474,473,475,477,478,476,487,486,485,490,488,489,435,437,436,433,434,432,469,468,467,471,472,470,506,508,507,503,504,505,608,610,611,607,612,609,619,645,647,700,674,678,696,679,698,697,691,702,705,706,187,186,188,189,190,191,71,66,67,68,69,70,144,149,145,146,147,148,150,155,151,152,153,154,57,56,58,59,54,55,75,74,76,77,72,73,45,44,46,47,42,43,22,21,23,18,19,20,115,114,116,117,118,119,129,128,130,131,126,127,53,52,48,49,50,51,361,360,362,364,365,363,393,395,394,392,390,391,511,510,509,514,512,513,538,537,536,533,534,535,544,543,542,541,539,540,400,399,401,397,398,396,515,517,516,519,520,518,590,588,589,592,593,591,565,564,566,568,569,567,615,614,606,618,649,648,642,636,640,681,680,687,675,661,667,666,668,682,690,699,219,218,220,221,216,217,254,255,256,257,252,253,237,236,238,239,234,235,209,208,204,205,206,207,224,223,225,226,227,222,230,229,231,232,233,228,140,139,141,142,143,138,137,136,132,133,134,135,214,213,215,210,211,212,65,64,60,61,62,63,31,30,32,33,34,35,378,380,379,381,382,383,530,532,531,529,527,528,579,581,580,577,576,578,337,336,338,341,339,340,605,604,603,602,601,600,403,402,404,406,407,405,502,501,500,497,498,499,522,521,523,524,525,526,586,584,582,585,587,583,627,646,621,644,634,638,635,641,643,692,676,688,694,660,671,677,659,693,684,701,90,95,91,92,93,94,179,174,175,176,177,178,259,258,260,261,262,263,300,301,302,303,304,305,28,27,29,24,25,26,314,313,315,316,317,312,242,241,243,244,245,240,40,39,41,36,37,38,12,17,13,14,15,16,125,124,120,121,122,123,88,87,89,84,85,86,556,558,557,559,560,561,571,570,572,573,574,575,461,463,462,464,465,466,551,552,562,554,555,553,445,444,446,448,449,447,373,372,374,376,377,375,451,450,563,452,453,454,460,459,458,456,457,455,594,595,596,598,599,597,637,617,622,613,620,616,639,651,650,703,670,683,704,658,665,685,664,686,689,695,3,2,4,5,1,0,166,167,162,163,164,165,173,172,168,169,170,171,185,184,180,181,182,183,326,328,327,324,325,329,270,271,272,273,274,275,7,6,8,9,10,11,319,323,318,320,321,322,265,264,266,267,268,269,282,287,283,284,285,286,276,281,277,278,279,280,368,367,366,371,369,370,385,384,386,387,388,389,439,438,440,442,443,441,345,347,346,343,344,342,411,413,412,408,409,410,480,479,481,483,484,482,330,331,332,335,333,334,415,414,416,417,418,419,426,428,427,429,430,431,628,629,625,630,626,623,632,631,624,669,656,657,672,654,653,655,652,662,663,673 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#33d45c5563bf4abb244f69cfa51749fb5a869f311e4fb00d8e6c25812252a226, 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 2026-10-06 21:54:00 · history