Equation 677 Database

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Magma 5ca1f200cf37…

magma 5ca1f200cf37
Size
381
Isomorphism class hash
5ca1f200cf3717144c60335d5c5ffb7dcfe39cd5ab904ed5b48ee245d82185c0
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 23:45:50
Display reorder
380,47,46,45,1,273,213,27,28,240,24,25,26,218,223,228,233,238,288,116,105,110,101,290,96,296,7,6,4,5,3,320,318,319,323,321,322,84,71,76,281,86,90,245,251,256,260,265,275,156,161,151,170,175,165,140,145,135,126,131,120,188,183,193,198,203,208,366,348,356,338,333,360,371,350,341,375,18,2,0,17,270,211,51,52,243,48,49,50,215,220,225,231,236,286,117,107,112,102,292,97,295,22,23,21,19,20,311,309,310,308,306,307,82,73,78,282,87,92,248,254,258,262,267,277,157,162,152,172,177,167,142,147,137,127,132,122,186,181,191,195,200,205,367,346,355,336,330,362,372,352,342,377,34,11,9,33,272,212,43,44,242,40,41,42,217,222,227,232,237,287,115,106,111,100,291,95,297,38,39,37,35,36,300,302,301,304,305,303,80,72,77,280,85,91,247,252,257,261,266,276,155,160,150,171,176,166,141,146,136,125,130,121,187,182,192,197,202,207,365,347,357,337,332,361,370,351,340,376,59,12,13,58,274,214,68,69,244,65,66,67,219,224,229,234,239,289,118,108,113,103,293,98,299,63,64,62,60,61,314,312,313,317,315,316,83,74,79,283,88,93,249,253,259,263,268,278,158,163,153,173,178,168,143,148,138,128,133,123,189,184,194,199,204,209,368,349,359,339,334,363,373,353,343,378,16,15,14,8,271,210,29,10,241,32,30,31,216,221,226,230,235,285,119,109,114,104,294,99,298,56,57,55,53,54,327,328,326,324,325,329,81,70,75,284,89,94,246,250,255,264,269,279,159,164,154,174,179,169,144,149,139,129,134,124,185,180,190,196,201,206,369,345,358,335,331,364,374,354,344,379 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {75} 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 23:45:51 · history