Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 998cabdb87e2…

magma 998cabdb87e2
Size
705
Isomorphism class hash
998cabdb87e2ee9aec5d47a7058953385269236d39fcec2c7ff7cbe3cf932c4c
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 15:55:41
Display reorder
660,651,29,653,656,647,616,27,611,613,607,636,28,631,633,627,25,576,571,573,567,596,593,26,591,587,24,556,551,553,547,476,471,35,473,467,434,429,33,431,425,456,451,34,453,447,531,536,31,533,527,491,496,32,493,487,511,516,30,513,507,698,702,703,687,643,295,658,657,646,617,296,603,618,606,637,294,623,638,626,298,577,563,578,566,597,598,299,583,586,297,557,543,558,546,477,463,293,478,466,435,423,291,436,424,457,443,292,458,446,523,537,289,538,526,483,497,290,498,486,503,517,288,518,506,699,696,704,691,175,133,359,185,162,183,134,176,357,163,184,132,174,358,164,136,181,178,355,165,182,356,137,179,166,135,180,177,354,167,191,173,139,350,160,189,171,140,348,161,190,172,138,349,159,169,187,142,353,156,170,188,143,351,157,168,186,141,352,158,678,672,675,663,273,36,262,231,250,232,37,274,263,251,233,38,275,261,249,39,230,272,258,246,228,259,40,270,247,41,229,271,260,248,237,264,42,253,241,238,265,43,254,242,239,266,44,252,240,267,236,45,256,244,268,234,46,257,245,269,235,47,255,243,665,671,669,668,642,73,644,649,645,609,74,602,604,605,629,72,622,624,625,76,569,562,564,565,589,584,77,582,585,75,549,542,544,545,469,462,79,464,465,427,437,80,438,439,449,442,78,444,445,522,529,82,524,525,482,489,83,484,485,502,509,81,504,505,694,688,685,693,655,11,650,659,641,619,9,615,610,600,639,10,635,630,621,7,579,575,570,561,599,590,8,595,581,6,559,555,550,540,479,475,2,470,460,420,433,1,428,422,459,455,0,450,440,535,539,5,530,521,495,499,3,490,480,515,519,4,510,500,701,692,686,697,652,91,648,640,654,601,92,612,608,614,620,90,632,628,634,94,560,572,568,574,580,588,95,592,594,93,541,552,548,554,461,472,89,468,474,421,430,87,426,432,441,452,88,448,454,532,520,85,528,534,492,481,86,488,494,512,501,84,508,514,690,689,695,700,335,59,315,419,371,417,57,333,316,369,418,58,334,317,370,55,415,331,314,367,416,312,56,332,368,54,414,330,313,366,410,326,50,321,362,408,324,48,322,360,409,325,49,323,361,329,413,53,320,365,327,411,51,318,363,328,412,52,319,364,684,681,673,664,199,148,347,209,220,207,149,200,345,221,208,147,198,346,219,144,205,202,343,216,206,344,145,203,217,146,204,201,342,218,215,197,154,338,226,213,195,155,336,227,214,196,153,337,225,193,211,150,341,222,194,212,151,339,223,192,210,152,340,224,676,670,679,683,130,282,383,14,311,12,283,131,381,309,13,284,129,382,310,285,17,126,379,307,15,380,286,127,308,287,16,128,378,306,20,121,280,374,302,18,122,281,372,300,19,120,279,373,301,124,23,276,377,305,125,21,277,375,303,123,22,278,376,304,662,674,661,666,395,70,407,98,109,96,71,393,405,110,97,69,394,406,108,66,101,391,403,112,99,404,67,392,113,68,100,390,402,111,104,386,61,398,115,102,384,62,396,116,103,385,60,397,114,389,107,64,401,118,387,105,65,399,119,388,106,63,400,117,667,680,682,677 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#24d4369d63c88701266d916dc6f9c75e12853e26a0a22f3b011b6cf68ccd31bb, 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 15:55:42 · history