Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 1c84bc98118a…

magma 1c84bc98118a
Size
381
Isomorphism class hash
1c84bc98118aa8343eeb3b489fe5f3d5ef3635296701d061bcfa25a2ac7a1750
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 23:39:19
Display reorder
380,263,258,253,240,248,235,92,282,87,107,97,102,62,277,67,74,77,84,111,116,121,125,286,131,13,273,12,53,58,48,307,329,306,310,308,309,196,200,190,181,186,175,221,226,231,205,211,216,146,135,140,290,2,3,23,32,28,43,268,38,295,166,171,150,155,160,371,352,347,338,360,365,343,356,333,375,261,256,251,241,245,236,91,280,86,106,95,100,61,275,66,71,75,80,110,115,120,126,285,130,7,270,6,51,56,45,305,303,304,302,301,300,195,201,191,180,185,176,222,225,230,206,210,215,145,136,141,291,0,1,20,30,25,41,265,36,296,165,170,151,156,161,370,350,345,335,361,366,340,355,331,376,260,255,250,242,246,237,90,281,85,105,96,101,60,276,65,73,76,83,114,119,124,129,289,134,4,271,5,50,55,46,323,324,325,326,327,328,199,204,194,184,189,179,224,229,234,209,214,219,149,139,144,294,18,19,21,31,26,40,266,35,299,169,174,154,159,164,374,351,346,336,364,369,341,359,330,379,264,259,254,244,249,239,94,284,89,109,99,104,64,279,69,72,79,82,113,118,123,128,288,133,14,274,15,54,59,49,312,313,311,315,316,314,198,203,193,183,188,178,223,228,233,208,213,218,148,138,143,293,16,17,24,34,29,44,269,39,298,168,173,153,158,163,373,354,349,339,363,368,344,358,334,378,262,257,252,243,247,238,93,283,88,108,98,103,63,278,68,70,78,81,112,117,122,127,287,132,8,272,9,52,57,47,320,321,322,317,318,319,197,202,192,182,187,177,220,227,232,207,212,217,147,137,142,292,10,11,22,33,27,42,267,37,297,167,172,152,157,162,372,353,348,337,362,367,342,357,332,377 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#a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f, M = {76} 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 23:39:20 · history