Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma b6318b290d75…

magma b6318b290d75
Size
381
Isomorphism class hash
b6318b290d75c683a9aa34ba6d8323e18d802bc2976c8e50134117f111b89852
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 23:48:30
Display reorder
380,28,53,33,38,43,48,143,148,153,158,163,168,128,133,138,113,118,123,88,93,98,103,108,83,302,303,304,305,301,300,18,3,293,23,8,13,284,288,263,268,273,277,258,233,238,243,248,253,203,208,213,218,223,228,198,178,183,193,188,173,73,78,58,63,68,298,333,360,368,372,353,348,343,338,358,378,26,50,31,36,41,45,140,146,151,156,161,166,126,131,136,111,115,120,86,91,96,101,106,80,325,326,327,328,329,324,16,1,290,20,6,11,282,286,260,266,271,276,255,231,235,240,245,250,200,206,211,216,221,226,195,175,180,190,185,171,70,75,55,60,65,295,330,363,366,374,351,346,341,336,356,375,25,51,30,35,40,46,141,145,150,155,160,165,125,130,135,110,116,121,85,90,95,100,105,81,309,310,311,306,307,308,15,0,291,21,5,10,281,285,261,265,272,275,256,230,236,241,246,251,201,205,210,215,220,225,196,176,181,191,186,170,71,76,56,61,66,296,331,361,365,371,350,345,340,335,355,370,27,52,32,37,42,47,142,147,152,157,162,167,127,132,137,112,117,122,87,92,97,102,107,82,322,323,318,319,320,321,17,2,292,22,7,12,283,287,262,267,270,278,257,232,237,242,247,252,202,207,212,217,222,227,197,177,182,192,187,172,72,77,57,62,67,297,332,364,367,376,352,347,342,337,357,377,29,54,34,39,44,49,144,149,154,159,164,169,129,134,139,114,119,124,89,94,99,104,109,84,317,312,313,314,315,316,19,4,294,24,9,14,280,289,264,269,274,279,259,234,239,244,249,254,204,209,214,219,224,229,199,179,184,194,189,174,74,79,59,64,69,299,334,362,369,373,354,349,344,339,359,379 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 = {66} 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 23:48:30 · history