Equation 677 Database

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Magma 9a246ad48564…

magma 9a246ad48564
Size
381
Isomorphism class hash
9a246ad48564dd8e97d3d084636d194a2ace0d774da95df90ca718a1de120f31
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 23:38:18
Display reorder
380,31,33,28,29,30,41,20,42,21,43,127,142,144,139,140,141,124,125,126,128,193,177,194,189,190,191,174,175,176,178,243,227,244,239,240,241,224,225,226,228,308,302,327,303,309,77,92,94,89,90,91,74,75,76,78,294,277,292,289,290,291,274,275,276,278,326,368,339,375,344,347,367,376,338,346,345,18,39,40,19,17,34,36,49,48,35,146,120,121,122,123,119,145,147,148,149,170,196,171,172,173,169,195,197,198,199,221,246,220,222,223,219,245,247,248,249,306,307,301,300,305,97,70,71,72,73,69,95,96,99,98,271,296,270,272,273,269,295,297,299,298,315,377,365,341,340,366,378,350,379,349,348,8,9,10,11,38,25,46,26,47,27,137,110,111,112,113,109,134,135,136,138,160,187,161,162,163,159,184,185,186,188,211,237,210,212,213,209,234,235,236,238,320,321,322,323,324,87,60,61,62,63,59,84,85,86,88,261,287,260,262,263,259,284,285,286,288,325,374,361,335,342,362,373,354,351,353,352,23,22,45,44,24,1,2,37,32,0,100,130,129,133,132,131,101,102,103,143,180,150,179,182,183,181,151,152,153,192,229,200,230,233,232,231,202,201,203,242,316,329,311,328,312,50,80,79,83,82,81,51,52,53,93,279,252,280,283,282,281,251,253,250,293,310,356,372,369,357,371,330,343,355,370,358,4,5,6,7,3,12,13,14,16,15,117,105,106,107,108,104,114,115,116,118,155,167,156,157,158,154,164,165,166,168,206,217,205,207,208,204,214,215,216,218,304,318,313,319,317,67,55,56,57,58,54,64,65,66,68,256,267,255,257,258,254,264,265,266,268,314,364,359,334,332,360,363,336,331,337,333 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#a5ceaca916191ef68f2e3b6b2367dcc497ee860690a383f5692cc65c6f41ad3d, 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 23:38:19 · history