Equation 677 Database

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Magma 7097de451175…

magma 7097de451175
Size
381
Isomorphism class hash
7097de4511757593fe11e48991d3ea1c1b69a1c5018fb70feea9210a855af005
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 23:31:50
Display reorder
380,106,105,107,102,103,104,73,62,65,67,69,71,115,117,0,2,3,1,28,29,24,25,26,27,290,295,271,276,280,285,201,205,181,186,191,196,111,112,113,108,109,110,216,221,226,231,235,211,252,257,262,267,242,247,325,326,327,328,329,324,150,176,155,161,166,171,355,376,343,337,335,351,347,370,366,364,54,146,55,134,138,142,44,45,46,47,42,43,49,50,51,52,53,48,30,31,32,33,34,35,294,299,274,279,283,289,204,208,183,188,193,198,41,36,37,38,39,40,218,223,228,234,238,213,253,258,264,268,243,248,301,300,302,303,304,305,154,179,159,163,169,174,358,378,345,344,341,334,338,373,368,360,114,98,116,99,100,101,89,90,91,86,87,88,95,96,97,92,93,94,80,81,82,83,84,85,291,296,270,275,281,286,200,206,180,185,190,195,74,75,76,77,78,79,215,220,225,230,236,210,250,255,260,265,241,246,316,317,312,313,314,315,151,175,156,160,165,170,356,375,349,350,331,332,330,371,365,363,10,147,11,135,139,143,18,19,20,21,22,23,15,16,17,12,13,14,64,66,68,70,72,63,293,298,273,278,284,288,203,209,184,189,194,199,56,57,58,59,60,61,219,224,229,233,239,214,254,259,263,269,244,249,306,307,308,309,310,311,153,178,158,164,168,173,359,379,339,346,348,340,342,374,369,361,123,122,124,125,120,121,119,137,140,144,148,118,136,141,145,149,132,133,127,128,129,130,131,126,292,297,272,277,282,287,202,207,182,187,192,197,7,8,9,4,5,6,217,222,227,232,237,212,251,256,261,266,240,245,318,319,320,321,322,323,152,177,157,162,167,172,357,377,333,353,354,336,352,372,367,362 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, 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 23:31:51 · history