Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma cdee50f88497…

magma cdee50f88497
Size
381
Isomorphism class hash
cdee50f884970a0b707a272d8d13eb8eb489fb6179daa23165adb6f5894e7ae0
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 23:48:45
Display reorder
380,278,273,283,288,293,298,18,23,28,3,8,13,304,300,305,301,302,303,188,193,198,203,208,183,78,83,88,63,68,73,133,138,143,148,123,128,47,52,57,32,37,42,113,118,93,98,103,108,228,233,238,213,218,223,178,158,163,173,168,153,248,253,258,263,268,243,354,346,371,361,335,376,347,357,367,341,279,274,284,289,294,299,19,24,29,4,9,14,323,318,319,320,321,322,189,194,199,204,209,184,79,84,89,64,69,74,134,139,144,149,124,129,45,50,55,31,36,41,114,119,94,99,104,109,229,234,239,214,219,224,179,159,164,174,169,154,249,254,259,264,269,244,350,348,372,362,339,377,349,359,368,337,277,272,282,287,292,297,15,20,25,0,5,10,312,313,314,315,316,317,186,191,196,201,205,181,75,80,85,61,66,71,130,135,140,145,121,126,48,53,58,33,38,43,112,117,92,97,102,107,226,231,236,210,215,220,175,156,161,170,166,151,245,250,255,260,265,240,352,344,373,363,345,378,333,358,366,334,275,271,280,285,290,295,17,22,27,2,7,12,329,324,325,326,327,328,187,192,197,202,207,182,77,82,87,62,67,72,132,137,142,147,122,127,49,54,59,34,39,44,111,115,91,96,101,106,227,232,237,212,217,222,177,157,162,172,167,152,247,252,257,262,267,242,353,340,370,364,336,375,338,355,365,332,276,270,281,286,291,296,16,21,26,1,6,11,308,309,310,311,306,307,185,190,195,200,206,180,76,81,86,60,65,70,131,136,141,146,120,125,46,51,56,30,35,40,110,116,90,95,100,105,225,230,235,211,216,221,176,155,160,171,165,150,246,251,256,261,266,241,351,331,374,360,343,379,330,356,369,342 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#e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378, M = {69} 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 23:48:46 · history