Equation 677 Database

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Magma 15931f0b3632…

magma 15931f0b3632
Size
381
Isomorphism class hash
15931f0b36325e50206b32d06b7d2a8ddcefe6942b79c7d3a22a02c5dad8eb40
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 23:33:40
Display reorder
380,114,119,115,116,117,118,107,102,103,104,105,106,199,209,218,229,239,189,269,279,289,299,249,259,305,301,300,302,303,304,21,22,23,18,19,20,274,284,294,243,254,264,111,112,113,108,109,110,99,100,101,96,97,98,213,224,234,184,194,204,17,16,12,13,14,15,368,337,367,333,351,374,350,336,349,379,1,5,0,2,3,4,41,36,37,38,39,40,196,206,215,226,236,186,266,276,286,296,245,256,318,319,320,321,322,323,123,124,125,120,121,122,272,282,290,241,252,262,10,11,6,7,8,9,47,42,43,44,45,46,212,222,232,182,192,202,126,131,127,128,129,130,364,352,363,335,334,372,341,353,340,376,34,33,35,30,31,32,66,67,68,69,70,71,197,207,216,227,237,187,267,277,287,297,246,257,311,306,307,308,309,310,83,78,79,80,81,82,275,285,295,244,255,265,24,25,26,27,28,29,62,63,64,65,60,61,214,225,235,185,195,205,75,74,76,77,72,73,366,346,365,338,339,375,345,347,344,377,92,91,93,94,95,90,151,152,153,154,155,150,191,201,210,220,230,181,261,271,281,291,248,251,314,315,316,317,312,313,139,140,141,142,143,138,273,283,293,242,253,263,88,89,84,85,86,87,144,145,146,147,148,149,219,223,233,183,193,203,132,137,133,134,135,136,362,354,360,332,348,373,355,330,331,371,160,159,161,156,157,158,178,179,174,175,176,177,190,200,211,221,231,180,260,270,280,292,240,250,327,328,329,324,325,326,54,55,56,57,58,59,278,288,298,247,258,268,165,166,167,162,163,164,172,173,168,169,170,171,217,228,238,188,198,208,49,48,50,51,52,53,361,343,369,356,357,378,359,342,358,370 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, 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 23:33:41 · history