Equation 677 Database

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Magma 5eabb025de8e…

magma 5eabb025de8e
Size
381
Isomorphism class hash
5eabb025de8e6aa91c022cb08f7c5a9c013397ce46c208571b1e46702247c8b3
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 23:30:43
Display reorder
380,238,243,328,324,177,192,92,102,272,264,142,122,57,62,67,77,82,15,3,8,172,147,48,38,203,208,218,228,248,252,329,327,326,325,282,182,187,197,97,87,107,112,292,277,268,258,132,137,117,127,72,21,12,233,162,167,152,157,53,27,43,33,213,223,288,295,342,332,373,337,352,347,377,357,363,365,235,241,310,306,175,190,91,100,273,261,140,121,55,61,66,76,80,16,0,5,171,145,45,36,200,205,216,226,246,253,311,309,308,307,281,181,185,195,96,85,106,110,293,278,266,256,130,136,115,126,70,22,13,230,160,166,151,156,51,25,40,31,210,221,286,297,340,330,371,335,353,345,376,355,361,367,239,244,315,314,179,194,94,104,274,263,144,124,59,64,69,79,84,18,4,9,174,149,49,39,204,209,219,229,249,254,316,317,313,312,284,184,189,199,99,89,109,114,294,279,269,259,134,139,119,129,74,24,14,234,164,169,154,159,54,29,44,34,214,224,289,299,344,334,374,339,354,349,379,359,364,369,236,240,301,305,176,191,90,101,270,260,141,120,56,60,65,75,81,19,2,7,170,146,46,37,201,206,215,225,247,250,300,302,304,303,280,180,186,196,95,86,105,111,290,275,265,255,131,135,116,125,71,20,10,231,161,165,150,155,50,26,41,32,211,220,285,296,341,331,370,336,350,346,375,356,360,366,237,242,323,319,178,193,93,103,271,262,143,123,58,63,68,78,83,17,1,6,173,148,47,35,202,207,217,227,245,251,321,322,318,320,283,183,188,198,98,88,108,113,291,276,267,257,133,138,118,128,73,23,11,232,163,168,153,158,52,28,42,30,212,222,287,298,343,333,372,338,351,348,378,358,362,368 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, M = {66} 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 23:30:45 · history