Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 17dfd9742771…

magma 17dfd9742771
Size
705
Isomorphism class hash
17dfd97427718a2d67d6c22df315188dc454ed4d18c4badaee0ac2609d76ff33
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 19:15:39
Display reorder
660,537,425,331,75,315,426,76,538,332,313,77,424,536,333,314,540,428,330,74,311,328,429,541,72,312,539,427,329,73,310,431,543,337,81,306,432,544,338,82,304,430,542,339,83,305,546,434,336,80,309,547,435,334,78,307,545,433,335,79,308,674,679,684,676,205,184,37,221,214,182,222,203,38,212,223,183,204,36,213,208,180,40,224,210,41,181,206,225,211,207,179,39,226,209,175,200,43,227,220,173,201,44,228,218,174,202,42,229,219,199,178,46,230,216,197,176,47,231,217,198,177,45,232,215,666,661,672,664,50,549,22,413,585,550,414,48,23,586,412,548,49,21,584,53,552,18,416,588,19,553,51,417,589,52,551,20,415,587,555,56,13,419,591,556,54,14,420,592,554,55,12,418,590,59,558,16,422,594,57,559,17,423,595,58,557,15,421,593,675,686,680,685,505,295,288,461,167,293,462,506,289,165,460,294,504,287,166,508,298,291,464,163,292,296,509,465,164,507,297,290,463,162,301,511,286,467,171,299,512,284,468,169,300,510,285,466,170,646,644,282,649,648,658,654,283,656,652,513,302,281,469,168,704,697,700,703,342,561,322,254,597,562,255,340,323,598,256,560,341,324,596,345,564,325,253,600,326,565,343,251,601,344,563,327,252,599,567,348,320,245,603,568,346,321,246,604,566,347,319,247,602,351,570,316,248,606,349,571,317,249,607,350,569,318,250,605,692,694,691,693,151,398,279,379,573,399,380,152,280,574,381,397,150,278,572,154,394,275,378,576,276,395,155,376,577,153,396,277,377,575,389,157,270,385,579,390,158,271,386,580,388,156,269,387,578,160,392,273,384,582,161,393,274,382,583,159,391,272,383,581,667,669,670,663,145,267,87,359,113,268,360,146,88,111,358,266,144,89,112,148,263,86,362,109,84,264,149,363,110,147,265,85,361,108,258,143,93,357,119,259,141,94,355,117,257,142,95,356,118,139,261,92,353,115,140,262,90,354,116,138,260,91,352,114,689,695,696,690,481,449,375,437,633,450,438,482,373,634,436,448,480,374,632,484,452,371,440,636,372,453,485,441,637,483,451,370,439,635,455,487,366,443,639,456,488,364,444,640,454,486,365,442,638,490,458,369,446,642,491,459,367,447,643,489,457,368,445,641,677,688,681,678,471,137,8,121,515,135,122,472,6,516,120,136,470,7,514,474,133,11,124,518,9,134,475,125,519,473,132,10,123,517,131,477,3,127,521,129,478,4,128,522,130,476,5,126,520,651,650,2,645,647,657,653,1,655,659,479,172,0,303,523,698,701,699,702,64,193,243,27,621,191,28,65,244,622,29,192,63,242,620,60,196,239,26,624,240,194,61,24,625,62,195,241,25,623,188,70,234,33,627,189,71,235,34,628,190,69,233,35,626,66,187,237,32,630,67,185,238,30,631,68,186,236,31,629,668,671,662,665,401,609,99,525,493,610,526,402,100,494,524,608,400,101,492,404,612,98,528,496,96,613,405,529,497,403,611,97,527,495,615,407,105,531,499,616,408,106,532,500,614,406,107,530,498,410,618,104,534,502,411,619,102,535,503,409,617,103,533,501,683,682,673,687 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#966159413732cc97ab9cbe48ea19b17c045c0e7dae7d4f88fdd62e86aa428734, 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 19:15:40 · history