Equation 677 Database

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Magma d2eac05e2856…

magma d2eac05e2856
Size
381
Isomorphism class hash
d2eac05e2856a3bee51c5efe0ee071b7e790643aea041fe02e3e0358192c4afa
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 23:22:53
Display reorder
380,251,260,257,245,237,240,200,191,196,185,175,182,141,290,145,126,131,136,22,12,16,7,267,2,100,105,110,116,121,285,55,61,50,275,71,66,323,321,322,320,318,319,225,231,220,211,216,206,30,270,25,46,35,41,155,160,151,171,295,166,90,95,281,86,76,81,332,372,355,360,365,351,340,337,345,377,250,262,255,246,235,241,202,192,197,187,177,180,140,291,146,125,130,135,21,11,19,5,266,0,102,107,112,117,122,287,57,62,52,277,72,67,324,325,326,327,328,329,226,230,221,210,215,207,32,272,27,47,37,42,156,161,150,170,296,165,92,97,282,87,77,82,330,371,357,361,366,352,342,336,347,376,253,264,259,249,239,244,204,194,199,189,179,184,144,294,149,129,134,139,24,14,18,9,269,4,104,109,114,119,124,289,59,64,54,279,74,69,304,305,303,300,302,301,229,234,224,214,219,209,34,274,29,49,39,44,159,164,154,174,299,169,94,99,284,89,79,84,334,374,359,364,369,354,344,339,349,379,254,261,256,248,238,243,203,193,198,188,178,183,143,293,148,128,133,138,23,13,17,8,268,3,103,108,113,118,123,288,58,63,53,278,73,68,308,306,307,311,309,310,228,233,223,213,218,208,33,273,28,48,38,43,158,163,153,173,298,168,93,98,283,88,78,83,333,373,358,363,368,353,343,338,348,378,252,263,258,247,236,242,201,190,195,186,176,181,142,292,147,127,132,137,20,10,15,6,265,1,101,106,111,115,120,286,56,60,51,276,70,65,315,316,317,312,313,314,227,232,222,212,217,205,31,271,26,45,36,40,157,162,152,172,297,167,91,96,280,85,75,80,331,370,356,362,367,350,341,335,346,375 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, M = {69} 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 23:22:54 · history