Equation 677 Database

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Magma eb9240d34628…

magma eb9240d34628
Size
399
Isomorphism class hash
eb9240d34628b6dc510e27b10aeaa58425317b74e02ac545bedb8220ee76846c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 15:31:07
Display reorder
300,301,302,303,304,305,297,298,299,293,294,295,296,288,289,290,291,292,381,264,308,279,327,328,265,309,280,266,329,310,281,267,330,311,282,312,268,331,283,332,269,313,284,261,324,314,285,325,262,306,286,326,263,307,287,317,336,257,272,318,337,258,273,319,338,259,274,320,339,260,275,321,340,252,276,322,341,253,277,323,333,254,278,315,334,255,270,316,335,256,271,391,385,386,392,128,248,94,172,173,129,249,95,130,174,250,96,131,175,251,97,243,132,176,98,177,133,244,90,134,178,245,91,179,126,246,92,171,127,247,93,241,165,137,103,242,166,138,104,234,167,139,105,235,168,140,106,236,169,141,107,237,170,142,99,238,162,143,100,239,163,135,101,240,164,136,102,383,389,390,384,153,18,182,13,14,154,19,183,155,15,20,184,156,16,21,185,22,157,17,186,9,158,23,187,159,10,24,188,11,160,25,180,12,161,26,181,27,6,146,191,28,7,147,192,29,8,148,193,30,1,149,194,31,0,150,195,32,2,151,196,33,3,152,197,34,4,144,189,35,5,145,190,388,398,397,387,232,75,342,349,351,233,76,344,225,352,77,346,226,354,78,348,79,227,356,350,358,228,80,353,229,343,72,355,345,230,73,357,347,231,74,359,84,366,216,360,85,368,217,363,86,370,218,365,87,372,219,367,88,374,220,369,89,376,221,371,81,361,222,373,82,362,223,375,83,364,224,377,394,395,396,393,44,65,206,117,118,36,66,198,37,119,67,199,38,120,68,200,69,39,121,201,122,40,70,202,41,123,71,203,124,42,63,204,125,43,64,205,58,110,53,215,59,111,45,207,60,112,46,208,61,113,47,209,62,114,48,210,54,115,49,211,55,116,50,212,56,108,51,213,57,109,52,214,382,378,380,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#28eac71d3c31f47ee4b66c01d39d19e24537c9d0fa8a71b7531d6e4b77e50968, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-07 15:31:10 · history