Equation 677 Database

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Magma 45a6bc666af1…

magma 45a6bc666af1
Size
595
Isomorphism class hash
45a6bc666af151e81074edaf0dd4d55eaed6f4edd7ced995ce7ca5c0ba48b8bf
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 01:52:27
Display reorder
72,20,54,136,73,15,55,137,74,16,56,138,75,17,51,139,70,18,52,134,71,19,53,135,114,116,117,112,113,115,544,510,511,514,531,286,214,242,249,226,221,208,42,57,99,187,63,10,200,128,48,64,154,14,58,76,227,222,206,232,239,265,308,397,381,456,422,403,431,382,401,406,389,385,376,393,399,100,188,47,11,202,127,65,153,13,59,77,34,31,2,340,343,354,368,341,332,370,321,244,285,213,241,248,225,223,207,233,240,264,326,324,331,374,372,346,360,334,344,405,388,386,377,394,400,414,463,462,380,464,460,582,581,518,552,533,528,529,554,535,516,526,589,594,590,517,564,497,490,474,486,505,489,504,378,402,408,419,407,435,415,218,254,250,284,268,228,255,183,105,182,6,60,81,121,87,163,102,23,78,150,108,229,256,305,267,304,209,243,483,491,485,500,488,470,482,430,417,391,409,446,416,445,4,61,82,118,88,164,103,24,79,151,106,39,89,184,104,181,5,62,83,119,86,161,101,25,80,152,107,40,350,367,355,366,329,345,348,120,253,162,266,26,568,569,572,527,551,573,550,553,543,521,524,534,525,520,560,512,29,84,93,172,125,158,149,293,319,296,287,204,230,274,67,132,1,30,85,94,173,272,290,283,294,320,295,288,273,231,275,245,205,220,251,95,174,126,159,147,170,199,175,155,133,41,140,66,0,219,252,262,297,271,289,282,501,509,502,498,494,475,495,479,466,471,484,487,503,493,157,148,169,198,171,156,131,339,357,347,327,337,349,352,439,421,432,429,437,455,438,499,424,392,425,480,592,591,580,558,562,579,548,515,563,542,578,585,555,545,540,583,478,472,506,468,469,476,496,481,508,477,492,467,507,473,356,362,330,342,338,369,333,22,43,146,69,195,46,122,166,192,38,110,8,50,33,309,212,216,235,280,247,317,44,123,167,193,35,111,9,238,224,310,210,217,236,281,68,196,45,124,168,194,36,109,7,49,32,189,12,21,395,428,404,454,396,420,436,453,390,418,379,398,387,448,211,215,234,279,246,318,237,270,165,197,37,269,584,586,587,546,541,556,571,588,539,519,575,536,532,561,577,530,277,261,298,303,315,258,312,178,160,185,98,141,27,201,129,96,142,144,92,177,180,316,259,313,300,292,307,263,413,384,457,423,426,427,412,440,444,452,410,449,442,433,186,3,97,28,203,130,143,145,91,176,179,191,90,190,364,361,365,328,353,336,371,322,276,278,260,301,302,314,257,311,299,291,306,323,325,335,375,373,358,359,351,363,443,451,411,450,441,434,447,459,458,383,465,461,574,576,565,537,567,522,566,557,570,549,559,538,593,523,513,547 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#7e8aed28d13c6f01abd34430eeaaae8bb6e95d30748edf1c7706abbded10a524, M = the submagma generated by {0, 1} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 01:52:28 · history