Equation 677 Database

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Magma b4e7b14b302d…

magma b4e7b14b302d
Size
705
Isomorphism class hash
b4e7b14b302d90a7dbab198e25a73f0b3328695090ece40b80925fb000557fc8
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 19:43:14
Display reorder
660,55,303,421,339,301,304,56,422,340,299,54,302,420,338,300,51,306,424,342,297,52,307,425,343,298,53,305,423,341,296,61,309,345,427,292,62,310,346,428,290,60,308,344,426,291,312,57,348,430,295,313,58,349,431,293,311,59,347,429,294,675,678,673,680,66,198,246,369,525,199,67,247,370,526,68,197,248,371,524,65,194,249,368,528,63,195,250,366,529,64,196,251,367,527,72,189,360,244,531,73,190,361,245,532,74,188,362,243,530,192,71,363,240,534,193,69,364,241,535,191,70,365,242,533,661,672,667,665,50,327,207,585,433,328,48,208,586,434,49,326,206,584,432,46,330,210,588,436,47,331,211,589,437,45,329,209,587,435,41,333,591,205,439,39,334,592,203,440,40,332,590,204,438,336,44,594,201,442,337,42,595,202,443,335,43,593,200,441,677,686,681,682,260,276,176,505,273,274,258,174,506,271,259,275,175,504,272,263,279,172,508,269,261,277,173,509,270,262,278,171,507,268,255,282,511,180,266,256,280,512,178,264,257,281,510,179,265,644,254,647,648,649,655,252,658,652,654,283,253,513,177,267,704,700,703,698,103,138,537,481,597,139,104,538,482,598,102,140,536,480,596,99,137,540,484,600,100,135,541,485,601,101,136,539,483,599,109,144,487,543,603,110,145,488,544,604,108,146,486,542,602,143,105,490,546,606,141,106,491,547,607,142,107,489,545,605,689,692,694,693,213,409,573,457,164,410,214,574,458,162,212,408,572,456,163,216,412,576,460,160,217,413,577,461,161,215,411,575,459,159,219,415,463,579,170,220,416,464,580,168,218,414,462,578,169,418,222,466,582,166,419,223,467,583,167,417,221,465,581,165,664,666,670,669,75,26,230,445,116,24,76,231,446,114,77,25,232,444,115,78,22,233,448,112,79,23,234,449,113,80,21,235,447,111,81,17,451,228,122,82,15,452,229,120,83,16,450,227,121,20,84,454,224,118,18,85,455,225,119,19,86,453,226,117,695,690,696,691,36,469,315,633,385,470,37,316,634,386,38,468,314,632,384,35,472,318,636,388,33,473,319,637,389,34,471,317,635,387,27,475,639,321,391,28,476,640,322,392,29,474,638,320,390,478,30,642,324,394,479,31,643,325,395,477,32,641,323,393,683,688,679,676,124,185,288,516,351,186,125,289,514,352,123,187,287,515,350,127,184,284,519,354,128,182,285,517,355,126,183,286,518,353,130,2,522,239,357,131,1,520,237,358,129,0,521,238,356,650,133,651,645,646,653,134,659,656,657,181,132,523,236,359,702,701,697,699,13,397,561,373,621,398,14,562,374,622,12,396,560,372,620,9,400,564,376,624,10,401,565,377,625,11,399,563,375,623,4,403,379,567,627,5,404,380,568,628,3,402,378,566,626,406,7,382,570,630,407,8,383,571,631,405,6,381,569,629,663,662,671,668,150,493,609,549,98,494,151,610,550,96,152,492,608,548,97,149,496,612,552,94,147,497,613,553,95,148,495,611,551,93,156,499,555,615,89,157,500,556,616,87,158,498,554,614,88,502,155,558,618,92,503,153,559,619,90,501,154,557,617,91,684,685,674,687 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#a559a3aef5c48d7617a1f37068ce834508ecbb6c78b3262065881b6dd2cda018, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 19:43:15 · history