Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 5d56a3e30265…

magma 5d56a3e30265
Size
381
Isomorphism class hash
5d56a3e30265ed088a87e4a3e42d041fe9190005166037f5281caa34d6f0b506
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 23:25:38
Display reorder
380,210,235,215,220,225,230,280,285,290,295,270,275,115,116,117,118,119,114,124,125,120,121,122,123,98,99,100,101,96,97,191,198,200,206,181,186,261,266,241,246,251,256,166,171,175,151,155,161,311,312,313,314,315,316,107,102,103,104,105,106,110,112,108,111,113,109,377,363,336,367,337,354,372,332,355,335,213,238,218,223,228,233,283,288,293,298,273,278,7,8,9,10,11,6,20,21,22,23,18,19,24,25,26,27,28,29,193,197,203,208,183,188,263,268,243,248,253,258,168,173,178,153,158,163,310,307,308,306,329,309,34,35,30,31,32,33,13,15,17,14,16,12,378,360,343,365,349,347,373,348,340,334,212,237,217,222,227,232,282,287,292,297,272,277,57,58,59,54,55,56,63,64,65,60,61,62,39,40,41,36,37,38,192,195,202,207,182,187,262,267,242,247,252,257,165,170,176,150,156,160,300,302,303,304,305,301,44,45,46,47,42,43,48,50,52,49,51,53,375,364,338,369,342,350,370,331,351,330,211,236,216,221,226,231,281,286,291,296,271,276,94,95,90,91,92,93,68,69,70,71,66,67,72,73,74,75,76,77,190,196,201,205,180,185,260,265,240,245,250,255,167,172,177,152,157,162,321,322,317,318,319,320,82,83,78,79,80,81,88,84,86,89,85,87,376,361,358,368,353,352,371,333,341,344,214,239,219,224,229,234,284,289,294,299,274,279,146,147,148,149,144,145,131,126,127,128,129,130,133,134,135,136,137,132,194,199,204,209,184,189,264,269,244,249,254,259,169,174,179,154,159,164,326,327,328,323,324,325,141,142,143,138,139,140,4,1,2,5,0,3,379,362,339,366,346,359,374,357,356,345 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#50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65, 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 23:25:39 · history