Equation 677 Database

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Magma 8f8344f6841b…

magma 8f8344f6841b
Size
381
Isomorphism class hash
8f8344f6841be240f4e6a4ef0bd953a362e50f645017381877727c5bd52d12d9
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 23:34:33
Display reorder
380,96,91,101,12,13,295,258,248,253,243,233,238,190,181,186,175,165,52,58,62,37,41,45,278,282,287,261,266,273,130,120,126,116,105,146,136,141,161,150,155,320,318,319,329,321,222,212,217,207,197,202,291,65,70,76,80,85,22,20,21,19,23,111,170,322,228,356,351,370,338,332,366,340,375,347,363,95,90,100,4,5,296,256,245,250,241,231,236,191,180,185,176,166,53,57,63,36,42,49,275,281,285,262,268,271,131,121,125,115,106,145,135,140,160,151,156,326,327,328,323,324,220,210,215,206,195,201,290,66,71,75,81,86,1,11,0,2,3,110,171,325,226,355,350,371,336,330,365,341,376,345,361,97,92,102,24,25,297,257,247,252,242,232,237,192,182,187,177,167,51,55,61,38,43,47,276,284,289,264,265,270,132,122,127,117,107,147,137,142,162,152,157,302,301,300,305,303,223,213,218,208,198,203,292,67,72,77,82,87,14,15,18,16,17,112,172,304,227,357,352,372,337,333,368,342,377,349,362,98,93,103,31,32,298,255,246,251,240,230,235,193,183,188,178,168,50,56,60,39,44,48,277,280,286,263,269,272,133,123,128,118,108,148,138,143,163,153,158,311,309,310,308,306,221,211,216,205,196,200,293,68,73,78,83,88,6,7,8,9,10,113,173,307,225,358,353,373,335,331,369,343,378,346,360,99,94,104,33,34,299,259,249,254,244,234,239,194,184,189,179,169,54,59,64,35,40,46,279,283,288,260,267,274,134,124,129,119,109,149,139,144,164,154,159,317,315,316,314,312,224,214,219,209,199,204,294,69,74,79,84,89,29,27,28,26,30,114,174,313,229,359,354,374,339,334,367,344,379,348,364 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#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, M = {68} 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 23:34:34 · history