Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma dacd7979812d…

magma dacd7979812d
Size
705
Isomorphism class hash
dacd7979812dab18114ab248c60ca9709d072309375dd2b3683fdba5a7ef33f8
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 15:19:18
Display reorder
704,488,323,355,344,356,321,342,486,487,322,354,343,491,319,358,347,489,320,359,345,490,318,357,346,353,339,314,483,351,340,312,484,352,341,313,485,338,349,317,482,336,350,315,480,337,348,316,481,335,333,334,331,332,330,326,324,328,329,327,325,675,673,672,674,94,248,239,226,237,246,227,95,93,247,238,225,90,251,235,222,91,249,236,223,92,250,234,224,230,217,243,85,228,218,244,86,229,216,245,84,220,233,242,88,221,231,240,89,219,232,241,87,261,262,263,260,258,259,252,253,257,255,256,254,664,666,667,665,370,285,273,495,274,286,496,371,369,287,275,497,366,284,272,494,367,282,270,492,368,283,271,493,264,501,276,361,265,502,277,362,266,503,278,360,500,267,279,364,498,268,280,365,499,269,281,363,648,649,650,651,652,653,654,655,658,656,657,659,686,684,687,685,33,57,45,83,46,58,81,34,35,59,47,82,32,56,44,79,30,54,42,80,31,55,43,78,36,74,48,24,37,72,49,25,38,73,50,26,77,39,51,27,75,40,52,28,76,41,53,29,68,66,67,71,69,70,63,64,61,62,60,65,701,703,702,700,585,609,647,633,645,610,634,586,587,611,646,635,584,608,643,632,582,606,644,630,583,607,642,631,638,624,600,576,636,625,601,577,637,626,602,578,627,641,603,579,628,639,604,580,629,640,605,581,620,618,619,623,621,622,615,616,613,614,612,617,689,691,690,688,289,390,422,409,420,391,410,290,288,392,421,408,292,393,425,412,293,394,423,413,291,395,424,411,428,415,388,295,426,416,389,296,427,414,387,294,418,431,384,298,419,429,385,299,417,430,386,297,400,401,399,396,397,398,406,407,404,402,403,405,662,661,660,663,111,149,135,123,136,147,124,112,113,148,137,125,110,145,134,122,108,146,132,120,109,144,133,121,141,129,155,117,142,130,153,118,143,131,154,119,128,140,151,116,126,138,152,114,127,139,150,115,159,160,161,158,156,157,165,166,163,164,162,167,694,693,692,695,376,505,540,534,541,506,535,377,375,504,542,536,372,508,543,537,373,509,544,538,374,507,545,539,546,532,511,382,547,533,512,383,548,531,510,381,528,549,514,378,529,550,515,379,530,551,513,380,519,520,521,518,516,517,525,526,523,524,522,527,682,683,680,681,100,191,172,208,173,189,209,101,99,190,171,207,96,187,168,204,97,188,169,205,98,186,170,206,178,214,182,106,179,215,180,107,177,213,181,105,210,174,185,102,211,175,183,103,212,176,184,104,202,203,201,198,199,200,193,194,195,196,197,192,696,698,697,699,596,559,23,4,21,560,5,594,595,558,22,3,599,562,19,1,597,563,20,0,598,561,18,2,14,10,557,591,12,11,555,592,13,9,556,593,6,17,553,590,7,15,554,588,8,16,552,589,564,565,566,567,568,569,570,571,575,573,574,572,671,668,669,670,305,459,451,443,452,460,441,303,304,461,450,442,301,458,454,439,302,456,455,440,300,457,453,438,449,434,465,311,447,432,466,309,448,433,467,310,437,445,464,307,435,446,462,308,436,444,463,306,468,469,470,471,472,473,474,475,479,477,478,476,676,678,679,677 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#14697465b8cd7575930ebcd6f1cfb0d098649f4474b7abfd50cfc1485faac906, 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 15:19:20 · history