Equation 677 Database

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Magma 39325a676a60…

magma 39325a676a60
Size
381
Isomorphism class hash
39325a676a60be118d8c8592953629568a4b50eb8ea23351c5f2b364949d332b
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 23:39:39
Display reorder
380,264,259,254,244,249,239,61,69,56,25,274,24,134,139,129,294,149,144,94,99,89,284,109,104,219,209,214,234,224,229,189,179,184,204,194,199,279,26,27,84,74,79,54,43,49,269,34,39,154,159,164,169,299,174,124,119,114,28,29,289,327,329,328,326,324,325,339,344,364,359,369,374,353,334,349,379,260,255,250,242,246,236,62,66,57,10,270,9,131,135,126,291,145,140,91,96,86,281,106,100,215,205,210,231,221,226,185,175,180,201,191,196,275,3,4,80,72,77,50,41,45,265,31,36,151,156,160,165,296,170,120,115,110,2,7,286,311,310,309,307,308,306,335,340,361,356,366,371,351,330,345,376,261,256,251,241,245,237,60,65,55,11,271,8,130,136,125,290,146,141,90,95,85,280,105,101,216,206,211,230,220,225,186,176,181,200,190,195,276,0,1,81,70,75,51,44,46,266,30,35,150,155,161,166,295,171,121,116,111,6,5,285,323,322,321,319,320,318,336,341,360,355,365,370,350,331,346,375,262,257,252,240,247,235,63,67,58,13,272,12,132,137,127,292,147,142,92,97,87,282,107,102,217,207,212,232,222,227,187,177,182,202,192,197,277,15,14,82,73,78,52,40,47,267,32,37,152,157,162,167,297,172,122,117,112,17,16,287,301,302,300,305,303,304,337,342,362,357,367,372,352,332,347,377,263,258,253,243,248,238,64,68,59,21,273,20,133,138,128,293,148,143,93,98,88,283,108,103,218,208,213,233,223,228,188,178,183,203,193,198,278,22,23,83,71,76,53,42,48,268,33,38,153,158,163,168,298,173,123,118,113,18,19,288,314,313,312,316,317,315,338,343,363,358,368,373,354,333,348,378 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 = {71} 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 23:39:40 · history