Equation 677 Database

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Magma aecbb01d37c5…

magma aecbb01d37c5
Size
705
Isomorphism class hash
aecbb01d37c5d25f7abad9d378904146745a10aca63f77584574f0b84fc2dabc
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 15:10:50
Display reorder
660,454,124,446,452,449,474,469,125,466,472,425,421,123,431,434,509,120,514,506,512,534,529,121,526,532,489,122,494,486,492,130,578,571,568,576,131,598,591,588,596,129,558,551,548,556,638,126,631,628,636,658,127,651,648,656,618,128,611,608,616,692,691,698,689,451,175,445,455,450,471,470,176,465,475,423,422,174,430,435,510,178,511,505,515,531,530,179,525,535,490,177,491,485,495,173,575,572,567,579,171,595,592,587,599,172,555,552,547,559,635,169,632,627,639,655,170,652,647,659,615,168,612,607,619,693,702,695,690,409,190,325,251,361,410,362,191,326,249,408,360,189,324,250,364,186,412,328,247,413,365,187,329,248,363,188,411,327,246,181,415,367,331,242,182,416,368,332,240,180,414,366,330,241,418,184,370,334,245,419,185,371,335,243,417,183,369,333,244,668,676,682,673,289,74,337,216,313,290,314,72,338,217,288,312,73,336,218,316,77,292,340,219,293,317,75,341,220,315,76,291,339,221,80,295,319,343,222,78,296,320,344,223,79,294,318,342,224,298,83,322,346,225,299,81,323,347,226,297,82,321,345,227,669,681,665,667,441,158,457,456,444,461,464,156,477,476,426,429,157,437,436,504,161,501,516,517,520,524,159,538,539,484,160,481,496,497,164,561,566,565,573,162,581,586,585,593,163,540,546,545,553,620,167,626,625,633,640,165,646,645,653,601,166,606,605,613,685,688,694,700,459,42,448,442,458,479,478,43,468,462,439,438,44,433,428,518,45,519,508,502,537,536,46,528,522,498,47,499,488,482,40,564,574,570,562,41,584,594,590,582,39,544,554,550,542,624,36,634,630,622,644,37,654,650,642,604,38,614,610,602,704,697,686,696,447,119,453,443,440,467,460,117,473,463,432,427,118,424,420,500,115,507,513,503,527,521,116,533,523,480,114,487,493,483,110,569,560,577,563,108,589,580,597,583,109,549,541,557,543,629,113,621,637,623,649,111,641,657,643,609,112,600,617,603,699,701,687,703,277,193,143,349,144,278,145,194,141,350,276,146,192,142,348,147,196,280,139,352,281,148,197,140,353,149,195,279,138,351,199,283,150,134,355,200,284,151,132,356,198,282,152,133,354,286,202,153,137,358,287,203,154,135,359,285,201,155,136,357,671,672,663,679,254,67,6,92,301,252,302,68,7,90,253,300,66,8,91,304,70,257,9,95,255,305,71,10,93,303,69,256,11,94,65,260,307,4,87,63,258,308,5,88,64,259,306,3,89,263,61,310,1,86,261,62,311,0,84,262,60,309,2,85,662,675,664,666,215,35,373,48,237,213,238,33,374,49,214,239,34,372,50,236,31,211,376,51,212,234,32,377,52,235,30,210,375,53,26,206,228,379,54,24,204,229,380,55,25,205,230,378,56,209,29,231,382,57,207,27,232,383,58,208,28,233,381,59,677,683,670,674,397,19,385,265,107,398,105,20,386,266,396,106,18,384,264,103,22,400,388,268,401,104,23,389,269,102,21,399,387,267,17,403,98,391,271,15,404,96,392,272,16,402,97,390,270,406,13,101,394,274,407,14,99,395,275,405,12,100,393,273,678,661,680,684 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#07e8f68f5124a8e3a0938e8678de1c72ed7349b338061e203d5db711c48e18fa, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 15:10:52 · history