Equation 677 Database

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Magma 8edf96b0cca2…

magma 8edf96b0cca2
Size
381
Isomorphism class hash
8edf96b0cca287157c63b84a67e4a83b01a8f4d47594c5966db7de1f453c4241
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 23:42:45
Display reorder
380,51,215,52,50,48,49,25,26,211,22,23,24,230,291,42,40,41,39,280,285,295,265,270,275,246,235,240,261,251,256,126,131,121,140,145,135,38,20,21,19,18,226,180,186,191,195,200,205,29,27,28,220,30,31,156,151,161,165,170,175,316,315,317,312,313,314,365,330,355,345,360,340,336,351,376,370,107,219,106,104,105,103,102,101,214,100,98,99,234,294,118,119,117,116,284,289,299,269,274,279,249,239,244,264,254,259,129,133,124,144,149,139,115,111,112,113,114,229,184,189,194,199,204,209,110,1,0,224,108,109,159,154,164,169,174,179,309,311,310,308,306,307,368,334,359,349,364,344,339,354,379,374,85,218,84,82,83,81,80,79,213,78,76,77,233,293,96,97,95,94,283,288,298,268,273,278,248,238,243,263,253,258,128,132,123,143,148,138,93,89,90,91,92,228,183,188,193,198,203,208,88,2,3,223,86,87,158,153,163,168,173,178,323,322,321,319,320,318,367,333,358,348,362,343,338,353,378,373,72,217,71,69,70,68,67,66,212,65,63,64,232,292,61,62,60,59,282,287,297,267,272,277,247,237,242,262,252,257,127,134,122,142,147,137,58,54,55,56,57,227,182,187,192,197,202,207,75,5,4,222,73,74,157,152,162,167,172,177,329,328,327,325,326,324,366,332,357,347,363,342,337,352,377,372,6,216,53,9,7,8,46,47,210,43,44,45,231,290,14,16,17,15,281,286,296,266,271,276,245,236,241,260,250,255,125,130,120,141,146,136,33,34,35,36,37,225,181,185,190,196,201,206,11,12,13,221,32,10,155,150,160,166,171,176,305,304,303,300,302,301,369,331,356,346,361,341,335,350,375,371 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, 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 23:42:46 · history