Equation 677 Database

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Magma a7befb90204e…

magma a7befb90204e
Size
401
Isomorphism class hash
a7befb90204e2b06ed9c7d123b624d09d8adfe8515a6f89b33fd073dcddb9a6a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 400) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 08:28:46
Display reorder
400,26,25,24,22,23,21,28,29,27,69,70,68,66,67,65,71,72,73,116,115,114,112,113,111,117,118,119,160,161,159,158,156,157,162,163,164,205,206,204,203,201,202,207,208,209,250,251,249,248,246,247,252,253,254,294,295,293,292,290,291,297,298,296,337,338,336,334,335,333,340,341,339,367,362,372,377,382,387,392,397,8,7,9,10,11,12,6,4,5,53,51,52,55,56,54,49,50,48,97,96,98,100,101,99,94,95,93,142,143,144,146,147,145,140,141,139,187,188,189,191,192,190,185,186,184,233,234,235,237,238,236,231,232,230,278,279,280,282,283,281,277,275,276,358,322,323,324,325,326,321,319,320,368,363,373,378,383,388,393,398,39,41,40,44,42,43,2,1,3,84,85,83,86,87,88,47,46,45,129,131,130,132,133,134,90,91,92,176,174,175,177,178,179,135,136,137,221,219,220,222,223,224,180,181,182,266,264,265,267,268,269,225,227,228,310,308,309,311,312,313,272,270,273,353,351,352,356,354,355,317,315,318,369,364,374,379,384,389,394,399,33,35,34,32,30,31,38,36,37,79,77,78,76,74,75,81,82,80,123,125,124,122,120,121,127,128,126,170,168,169,165,166,167,172,173,171,215,213,214,210,211,212,217,218,216,260,258,259,255,256,257,262,263,261,304,302,303,299,300,301,306,307,305,347,345,346,344,342,343,350,348,349,366,361,370,375,380,385,390,395,0,16,17,15,13,14,18,19,20,60,61,89,59,57,58,64,62,63,106,105,107,104,102,103,110,108,109,151,152,153,150,148,149,138,154,155,196,197,198,193,194,195,183,199,200,242,226,243,239,240,241,229,244,245,314,271,287,284,285,286,274,288,289,329,316,330,359,327,328,357,331,332,365,360,371,376,381,386,391,396 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 401 = 1 + 5*80, 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#0dd86070b42eb55a1a255aa4e6a7ee17e6a356f4c97ab7c8fc1c48e3adb556bb, M = {80} 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, 80): MacNeish's product over GF(16) x GF(5); GF(16) = F_2[x]/(x^4 + 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: 1.

last edited by qawbecrdtey at 2026-10-02 08:28:47 · history