Equation 677 Database

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Magma 36892043a492…

magma 36892043a492
Size
396
Isomorphism class hash
36892043a492a396a3b10f7aef7dc0aacf931f5d5959156fb626814bd90baa49
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 05:57:22
Display reorder
394,367,311,350,339,147,340,21,70,22,233,148,71,234,23,95,61,235,12,232,62,236,13,328,317,341,309,329,63,237,14,149,64,238,15,150,65,239,16,151,66,240,17,152,67,241,18,153,68,342,310,330,318,343,19,154,69,242,20,155,0,188,190,191,182,183,184,185,186,187,333,189,334,335,336,363,384,392,385,393,321,194,145,104,86,105,195,146,196,106,87,136,107,197,88,137,96,198,89,138,97,199,90,360,358,338,91,139,98,200,92,140,99,201,322,326,351,368,323,327,324,202,93,141,100,203,94,142,101,337,357,361,102,192,84,143,103,193,85,144,33,25,26,27,28,29,30,31,32,34,35,36,37,24,312,380,381,391,386,373,364,365,116,281,117,216,218,217,118,282,219,119,204,283,220,120,205,280,221,121,206,287,222,122,207,288,223,108,208,290,224,109,209,292,225,110,210,294,226,111,211,296,227,112,212,298,228,113,213,300,229,114,214,302,230,115,215,304,231,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,395,377,375,382,355,308,332,165,57,166,11,168,3,167,58,169,156,2,59,170,331,306,356,171,157,4,60,172,158,5,50,173,159,6,51,174,160,1,52,175,352,366,315,176,161,7,53,177,162,8,54,178,163,9,55,179,164,10,56,180,362,307,316,181,38,49,39,40,41,42,43,44,45,46,47,48,313,314,354,378,383,388,390,372,325,353,265,268,266,126,253,127,267,269,254,255,128,270,243,256,129,271,244,257,130,272,245,258,131,273,246,259,132,274,247,260,133,348,344,346,359,349,345,347,134,275,248,261,135,276,249,262,123,277,250,263,124,278,251,264,125,279,252,72,80,81,82,83,73,74,75,76,77,78,79,319,320,371,376,389,379,387 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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#7df1be11e8b03a352a732fe3cebbb8055958b1c7efe44dbc5799cf88069697db, 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, 79): MacNeish's product over GF(79); 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: 21.

last edited by qawbecrdtey at 2026-10-02 05:57:23 · history