Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma 1deaccd06c4e…

magma 1deaccd06c4e
Size
595
Isomorphism class hash
1deaccd06c4e0a54ab123a7c521fa0da3923f3507d290978fac78613be2ecea8
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
2026-10-06 09:24:46
Display reorder
306,311,307,308,309,310,506,504,507,508,509,505,472,471,467,468,469,470,448,447,443,444,445,446,271,272,270,274,275,273,555,572,571,594,578,320,322,321,318,319,323,461,466,462,463,464,465,374,373,375,376,377,372,346,345,347,342,343,344,450,449,451,452,453,454,337,336,338,339,340,341,314,313,315,316,317,312,86,85,84,89,87,88,73,72,74,77,75,76,69,71,70,68,66,67,259,258,257,256,254,255,102,104,103,107,105,106,202,201,200,198,199,197,94,93,95,91,92,90,11,10,9,7,8,6,218,219,267,217,215,216,539,534,514,519,527,549,544,550,520,577,560,588,583,593,570,565,398,503,396,400,397,399,501,500,502,497,498,499,288,293,289,290,291,292,439,438,440,441,442,437,432,431,433,434,435,436,408,407,409,410,411,412,413,418,414,415,416,417,56,55,54,59,57,58,124,123,125,122,120,121,141,143,142,140,138,139,224,223,225,221,222,220,96,98,97,101,99,100,185,184,183,180,182,181,12,14,13,15,16,17,176,174,175,178,179,177,263,265,264,262,260,261,537,531,511,517,526,546,542,554,524,575,557,586,581,591,568,563,280,277,281,278,279,276,385,384,386,387,388,389,490,489,485,486,487,488,456,455,457,458,459,460,327,326,328,329,324,325,428,427,429,430,425,426,369,368,370,371,366,367,46,45,47,43,44,42,79,78,80,83,81,82,38,37,36,40,41,39,238,242,239,241,268,240,167,166,165,162,164,163,188,190,189,187,186,209,5,4,3,2,1,0,127,126,128,129,130,131,253,252,269,249,250,251,535,532,510,516,525,547,541,552,523,573,558,584,579,589,566,561,424,420,419,422,423,421,401,406,402,403,404,405,351,350,352,353,348,349,363,362,364,365,360,361,296,295,297,298,299,294,492,491,493,494,495,496,303,302,304,305,300,301,118,117,119,115,116,114,62,61,60,63,64,65,53,52,51,49,50,48,233,232,234,236,237,235,168,170,169,173,171,172,204,203,205,206,207,208,109,108,110,112,113,111,149,148,147,145,146,144,228,227,226,230,231,229,538,533,513,518,528,545,543,551,521,576,559,587,582,592,569,564,480,482,481,484,479,483,354,359,355,356,357,358,332,331,333,334,335,330,383,382,378,379,380,381,390,395,391,392,393,394,285,284,286,287,282,283,474,473,475,476,477,478,135,137,136,132,133,134,18,20,19,22,23,21,24,26,25,29,27,28,247,246,248,244,245,243,156,157,158,159,160,161,192,191,193,194,195,196,152,151,150,155,153,154,32,31,30,34,35,33,211,210,266,213,214,212,536,530,512,515,529,548,540,553,522,574,556,585,580,590,567,562 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#20e9cec11ce1b4ef3a4be2ce0eb77a027f26009c155c08499f343b203c8ba1b3, M = the submagma generated by {0, 18} (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 2026-10-06 09:24:47 · history