Equation 677 Database

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Magma 99b5437f8ed6…

magma 99b5437f8ed6
Size
381
Isomorphism class hash
99b5437f8ed63599ef67284e4214f5127bb740f1ef8d68df0e8b2965bc74e7af
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 23:43:24
Display reorder
380,122,161,155,135,175,129,168,148,305,162,123,156,150,163,136,176,130,169,149,301,124,157,151,164,137,177,131,170,144,310,125,158,152,165,132,178,126,171,145,313,120,159,153,166,133,179,127,172,146,316,121,160,167,154,134,174,128,173,147,304,141,143,138,139,140,142,365,364,344,346,376,377,343,366,367,345,8,47,27,21,53,0,54,34,327,40,9,42,28,41,22,48,2,55,35,329,10,43,29,36,23,49,3,56,30,319,11,44,24,37,18,50,4,57,31,321,6,45,25,38,19,51,5,58,32,322,7,46,39,26,20,52,1,59,33,324,13,15,16,17,12,14,370,331,351,368,330,347,350,349,348,369,101,75,69,108,95,102,88,62,302,82,96,76,70,83,109,90,103,89,63,303,97,77,71,78,110,91,104,84,64,309,98,72,66,79,111,92,105,85,65,312,99,73,67,80,112,93,106,86,60,315,100,74,81,68,113,94,107,87,61,300,114,116,117,118,119,115,374,342,363,361,359,373,362,360,341,375,298,274,257,251,281,290,283,259,314,266,299,275,252,267,246,276,291,284,260,317,294,270,253,268,247,277,292,285,261,306,295,271,254,269,248,278,293,286,262,307,296,272,255,264,249,279,288,287,263,308,297,273,265,256,250,280,289,282,258,311,245,243,244,241,242,240,340,339,379,372,355,338,358,356,337,357,238,212,192,186,218,231,225,199,320,205,239,213,193,206,187,219,232,226,200,323,234,214,194,207,188,220,233,227,201,325,235,215,195,208,189,221,228,222,202,326,236,210,196,209,190,216,229,223,203,328,237,211,204,197,191,217,230,224,198,318,184,180,181,182,183,185,335,353,371,378,334,333,354,352,332,336 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#c6087800d19344ec7a4e6a4d71758b884911e8f7e7474c34d898093b3bb64a91, M = {66} 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 23:43:25 · history