Equation 677 Database

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Magma 6ddf71a4d07a…

magma 6ddf71a4d07a
Size
381
Isomorphism class hash
6ddf71a4d07a96294cfa7cbe3a1d2b8876f59174e80d3ffa09e961aa2afc83e9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:31:24
Display reorder
380,86,97,203,193,48,27,228,188,173,123,113,73,329,327,328,324,325,268,237,247,33,18,157,137,243,253,278,67,107,117,213,223,183,283,57,37,12,7,208,218,198,288,163,153,133,143,93,103,63,83,326,273,257,78,43,53,23,3,167,147,177,127,233,263,293,297,333,358,373,353,378,348,338,343,363,368,87,96,202,192,47,26,227,187,172,122,112,72,320,318,319,321,322,267,235,245,32,17,155,135,242,252,277,65,105,115,212,222,182,282,56,36,11,6,207,217,197,287,162,152,132,142,92,102,62,82,323,272,255,75,42,52,22,2,165,145,175,126,232,262,292,299,332,357,372,352,377,347,337,342,362,367,88,95,204,194,49,25,229,189,174,124,114,74,301,300,302,304,305,269,236,249,34,19,156,136,244,254,279,66,106,116,214,224,184,284,55,35,10,5,209,219,199,289,164,154,134,144,94,104,64,84,303,274,256,77,44,54,24,4,166,146,176,125,234,264,294,298,334,359,374,354,379,349,339,344,364,369,89,99,200,191,45,29,225,185,171,120,111,70,309,310,311,307,308,266,238,246,31,16,159,139,241,251,276,69,109,119,210,220,181,281,59,39,14,8,206,215,195,286,161,151,130,140,91,101,60,80,306,270,258,79,41,51,20,0,169,149,178,129,231,260,291,295,330,355,370,351,375,345,335,340,361,365,85,98,201,190,46,28,226,186,170,121,110,71,313,314,312,317,315,265,239,248,30,15,158,138,240,250,275,68,108,118,211,221,180,280,58,38,13,9,205,216,196,285,160,150,131,141,90,100,61,81,316,271,259,76,40,50,21,1,168,148,179,128,230,261,290,296,331,356,371,350,376,346,336,341,360,366 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, M = {74} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:31:25 · history