Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 55c0b88c4152…

magma 55c0b88c4152
Size
705
Isomorphism class hash
55c0b88c415278ecc7ad03b38bbe7543e0f912a0684ad64b0c607a821bde3617
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 17:26:00
Display reorder
660,277,303,235,455,288,278,304,236,456,289,276,305,234,457,290,280,302,238,454,291,281,300,239,452,292,279,301,237,453,293,233,283,309,461,294,231,284,310,462,295,232,282,311,463,296,286,229,308,460,297,287,230,306,458,298,285,228,307,459,299,663,670,661,665,599,125,219,132,443,600,123,220,133,444,601,124,221,134,445,598,121,218,135,442,596,122,216,136,440,597,120,217,137,441,225,605,131,138,449,226,606,129,139,450,227,607,130,140,451,604,224,127,141,448,602,222,128,142,446,603,223,126,143,447,685,689,687,688,261,3,39,583,107,262,4,40,584,105,263,5,38,585,106,260,2,42,582,103,258,1,43,580,104,259,0,41,581,102,37,252,9,589,98,35,253,10,590,96,36,254,11,591,97,255,33,8,588,101,256,34,6,586,99,257,32,7,587,100,669,662,668,671,172,419,154,368,491,173,420,155,369,492,171,421,153,370,493,168,418,150,371,490,169,416,151,372,488,170,417,152,373,489,145,178,425,374,497,146,179,426,375,498,144,177,427,376,499,174,148,424,377,496,175,149,422,378,494,176,147,423,379,495,675,683,678,673,479,383,157,182,511,480,384,158,180,512,481,385,156,181,513,478,382,160,185,510,476,380,161,183,508,477,381,159,184,509,163,485,389,188,517,164,486,390,186,518,162,487,391,187,519,484,166,388,191,516,482,167,386,189,514,483,165,387,190,515,664,666,667,672,250,523,29,315,559,251,524,30,316,560,249,525,31,317,561,246,522,28,314,558,247,520,26,312,556,248,521,27,313,557,20,241,529,321,565,21,242,530,322,566,22,240,531,323,567,244,23,528,320,564,245,24,526,318,562,243,25,527,319,563,697,696,698,694,503,595,90,95,507,630,631,91,629,628,632,635,89,634,633,504,594,86,94,502,505,592,87,92,500,506,593,88,93,501,81,649,651,650,648,82,653,655,654,652,80,656,659,658,657,644,84,647,646,645,637,85,639,638,636,641,83,643,642,640,704,701,702,703,14,335,61,198,327,15,336,59,199,328,16,337,60,200,329,17,334,57,201,326,18,332,58,202,324,19,333,56,203,325,67,622,341,196,623,65,624,342,197,625,66,627,343,195,626,620,63,340,192,621,12,64,338,193,330,13,62,339,194,331,695,699,700,693,274,535,74,571,611,275,536,75,572,612,273,537,76,573,613,270,534,77,570,610,271,532,78,568,608,272,533,79,569,609,72,265,541,577,617,73,266,542,578,618,71,264,543,579,619,268,68,540,576,616,269,69,538,574,614,267,70,539,575,615,680,676,684,682,402,467,204,431,407,403,468,205,432,408,401,469,206,433,409,398,466,207,430,406,399,464,208,428,404,400,465,209,429,405,210,393,473,437,413,211,394,474,438,414,212,392,475,439,415,396,213,472,436,412,397,214,470,434,410,395,215,471,435,411,677,679,674,681,116,348,45,359,547,114,349,46,360,548,115,347,44,361,549,119,344,48,358,546,117,345,49,356,544,118,346,47,357,545,51,111,354,365,553,52,112,355,366,554,50,113,353,367,555,110,54,350,364,552,108,55,351,362,550,109,53,352,363,551,690,691,692,686 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#555d8536a50144822bfea9b20f3ef68710f5792b887e6dda4840627962426043, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 17:26:01 · history