Equation 677 Database

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Magma 0f14447b1398…

magma 0f14447b1398
Size
381
Isomorphism class hash
0f14447b139816049731159b09f0297c0c167f308bc96c8446f590822d861899
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 23:15:52
Display reorder
380,276,270,286,255,261,266,233,238,228,248,298,243,128,133,138,143,148,153,78,84,254,88,93,98,50,51,52,53,54,223,168,158,163,183,173,178,47,48,218,45,49,46,317,315,316,314,312,313,212,202,207,197,187,192,57,56,283,59,58,55,290,121,115,106,111,101,332,350,348,358,338,363,343,369,373,378,277,272,287,257,262,267,231,236,226,245,295,240,126,131,136,140,145,150,76,82,252,86,91,95,4,5,6,7,8,221,166,157,162,181,170,175,17,18,215,14,15,16,328,329,327,325,326,324,210,200,205,196,185,191,27,26,280,29,28,25,292,122,117,107,114,102,330,352,345,355,335,361,341,366,370,375,275,271,285,256,260,265,230,235,225,246,296,241,127,132,137,142,147,152,75,81,250,85,90,96,20,21,22,23,24,220,167,156,161,182,172,177,3,2,216,0,19,1,305,303,304,302,301,300,211,201,206,195,186,190,10,9,281,31,30,11,291,120,116,105,112,100,331,351,346,356,336,362,340,365,372,376,278,273,288,258,263,268,232,237,227,247,297,242,129,134,139,144,149,154,77,83,253,87,92,97,13,12,39,37,38,222,169,159,164,184,174,179,36,35,217,34,32,33,323,321,322,320,318,319,213,203,208,198,188,193,40,42,282,44,43,41,293,123,118,108,110,103,333,353,347,357,337,364,342,367,374,377,279,274,289,259,264,269,234,239,229,249,299,244,125,130,135,141,146,151,79,80,251,89,94,99,65,66,67,68,69,224,165,155,160,180,171,176,62,63,219,60,64,61,308,306,307,311,309,310,214,204,209,199,189,194,72,71,284,74,73,70,294,124,119,109,113,104,334,354,349,359,339,360,344,368,371,379 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, 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 23:15:53 · history