Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 4156b325ecde…

magma 4156b325ecde
Size
705
Isomorphism class hash
4156b325ecde3a243d4f061ee56ede94efa392aa6e2134a6db5da113489ddeb5
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 18:10:59
Display reorder
660,312,510,512,509,515,535,530,313,532,529,490,495,314,492,489,435,315,430,432,429,316,453,451,452,450,475,317,470,472,469,630,318,635,632,629,319,655,652,650,649,320,615,612,610,609,555,321,552,550,549,575,322,572,570,569,595,323,592,590,589,696,692,686,694,113,507,514,511,516,536,527,111,534,531,487,496,112,494,491,436,109,427,434,431,110,459,457,458,446,476,108,467,474,471,627,119,636,634,631,117,656,654,647,651,118,616,614,607,611,556,115,554,547,551,576,116,574,567,571,596,114,594,587,591,688,691,693,685,163,412,89,136,236,234,413,164,87,137,411,235,162,88,135,239,166,408,85,132,167,237,409,86,133,238,165,410,84,134,418,161,231,95,142,159,232,93,419,143,160,233,94,417,141,230,157,91,414,138,228,158,92,415,139,229,156,90,416,140,664,681,669,677,206,182,376,38,307,308,180,204,377,36,181,306,205,375,37,310,209,185,372,41,207,311,183,373,39,309,208,184,374,40,188,212,305,382,44,210,303,383,186,42,211,304,381,187,43,301,215,378,191,47,302,213,379,189,45,300,214,380,190,46,668,678,661,671,105,503,504,513,508,528,523,106,524,533,483,488,107,484,493,428,104,423,424,433,102,445,443,444,447,468,103,463,464,473,623,96,628,624,633,97,648,644,643,653,98,608,604,603,613,548,99,544,543,553,568,100,564,563,573,588,101,584,583,593,689,702,697,703,21,519,517,506,518,538,539,22,537,526,499,498,23,497,486,438,20,439,437,426,18,441,442,440,448,477,19,479,478,466,639,12,637,638,626,13,658,657,659,646,14,617,618,619,606,558,15,557,559,546,578,16,577,579,566,597,17,598,599,586,690,701,695,687,30,502,505,500,501,521,522,31,525,520,482,481,32,485,480,420,33,422,425,421,34,454,455,456,449,461,35,462,465,460,622,28,620,625,621,29,640,645,642,641,27,601,605,602,600,541,24,545,542,540,561,25,565,562,560,581,26,585,582,580,700,704,698,699,291,223,11,154,81,82,224,292,9,155,222,83,293,10,153,80,290,226,7,150,288,78,227,8,151,79,289,225,6,152,221,297,72,2,145,298,73,1,219,146,299,74,0,220,144,75,296,5,217,148,76,294,3,218,149,77,295,4,216,147,679,672,675,682,177,200,352,54,388,389,198,178,353,55,199,387,179,351,56,384,176,203,348,57,174,385,201,349,58,386,175,202,350,59,195,168,394,358,52,169,395,359,196,53,170,393,357,197,51,390,171,354,194,48,391,172,355,192,49,392,173,356,193,50,673,683,684,666,63,123,240,364,269,267,124,64,241,365,125,268,65,242,363,265,62,122,243,360,60,266,120,244,361,264,61,121,245,362,129,69,275,246,370,70,273,247,130,371,71,274,248,131,369,271,68,249,128,366,272,66,250,126,367,270,67,251,127,368,676,680,667,662,260,279,400,340,328,329,280,258,401,341,281,327,259,399,339,324,263,278,396,336,261,325,276,397,337,326,262,277,398,338,285,255,334,406,346,256,335,407,286,347,257,333,405,287,345,330,254,402,284,342,331,252,403,282,343,332,253,404,283,344,663,670,665,674 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#6997491de262e367994a4a50c6f8055cb54c2a6a0260cea123f554e749c551e0, 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 18:11:00 · history