Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 49fcef51eeeb…

magma 49fcef51eeeb
Size
381
Isomorphism class hash
49fcef51eeeb0ed6fc5d6b330f7505c296f26c0780b4afb78f0c9bc31160a5d5
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 23:38:06
Display reorder
380,67,242,62,52,57,47,141,147,137,127,131,121,100,95,291,115,106,111,267,277,262,252,257,247,232,237,287,217,222,227,80,85,90,280,71,76,2,210,3,271,1,0,22,27,297,31,36,42,308,306,307,311,309,310,180,185,190,196,200,205,152,162,156,176,166,172,364,330,347,340,351,357,367,377,335,371,66,240,61,50,56,45,142,146,136,126,132,122,102,97,292,117,107,112,266,276,261,250,255,245,230,235,286,216,221,226,81,88,91,282,72,77,9,212,8,272,10,11,21,26,295,33,38,41,328,329,327,325,326,324,182,187,192,197,202,207,150,161,157,177,167,171,361,332,345,342,352,355,365,375,337,373,69,244,64,54,59,49,144,149,139,129,134,124,104,99,294,119,109,114,269,279,264,254,259,249,234,239,289,219,224,229,83,89,94,284,74,79,17,214,16,274,18,19,24,29,299,34,39,44,314,312,313,317,315,316,184,189,194,199,204,209,154,164,159,179,169,174,363,334,349,344,354,359,369,379,339,374,65,241,60,51,55,46,140,145,135,125,130,120,101,96,290,116,105,110,265,275,260,251,256,246,231,236,285,215,220,225,84,86,92,281,70,75,4,211,5,270,7,6,20,25,296,32,37,40,301,300,302,303,304,305,181,186,191,195,201,206,151,160,155,175,165,170,360,331,346,341,350,356,366,376,336,370,68,243,63,53,58,48,143,148,138,128,133,123,103,98,293,118,108,113,268,278,263,253,258,248,233,238,288,218,223,228,82,87,93,283,73,78,13,213,12,273,14,15,23,28,298,30,35,43,323,321,322,320,318,319,183,188,193,198,203,208,153,163,158,178,168,173,362,333,348,343,353,358,368,378,338,372 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, M = {75} 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 23:38:07 · history