Equation 677 Database

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Magma 57edb816bcc1…

magma 57edb816bcc1
Size
396
Isomorphism class hash
57edb816bcc16fc646f2358c9e9115006fcf7d1b00c4cfd84d8d8bf0a823201e
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 05:44:15
Display reorder
394,366,336,350,340,24,337,57,215,170,25,50,216,171,26,253,217,172,27,254,218,173,28,316,341,334,313,317,219,163,29,51,220,164,30,52,221,165,31,53,222,166,32,54,223,167,33,55,224,335,314,318,342,315,168,56,225,226,169,34,49,14,16,17,18,19,20,21,22,23,312,15,309,310,311,354,385,391,383,393,348,132,176,161,260,133,177,162,134,261,178,152,135,262,179,153,136,263,180,154,137,264,181,361,360,349,182,155,126,265,183,156,127,266,338,332,352,368,339,333,330,256,184,157,128,257,185,158,129,347,363,362,258,130,174,159,160,131,259,175,149,141,142,143,144,145,146,147,148,150,151,138,139,140,331,378,375,390,386,373,355,364,214,281,44,198,200,45,282,199,201,46,283,186,202,47,280,187,203,48,287,188,204,35,288,189,205,36,290,190,206,37,292,191,207,38,294,192,208,39,296,193,209,40,298,194,210,41,300,195,211,302,42,196,212,213,43,304,197,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,395,377,376,382,358,327,321,71,95,111,82,72,112,96,83,73,113,97,84,74,325,324,357,75,103,98,85,76,104,99,86,77,105,100,87,78,106,101,88,79,351,367,322,66,107,102,89,67,108,92,90,68,109,93,91,69,94,110,80,70,356,326,323,81,125,117,118,119,120,121,122,123,124,114,115,116,328,329,359,381,384,387,392,372,306,353,237,267,0,240,238,252,268,241,239,255,269,242,227,58,270,243,228,59,271,244,229,60,272,245,230,61,273,246,231,62,274,345,343,319,365,346,344,320,275,247,232,63,276,248,233,64,277,249,234,278,65,250,235,236,1,279,251,2,6,7,8,9,10,11,12,13,3,4,5,307,308,371,379,388,380,389 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#5ea0801c37b7140a4d0f8cc6cd6f875b6a59b1b3f8cb66e6f780ccb36bd56c74, 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 05:44:18 · history